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  5. 模型预测控制（MPC）在自动驾驶、机器人与工业过程控制领域的研究趋势报告

模型预测控制（MPC）在自动驾驶、机器人与工业过程控制领域的研究趋势报告

深度研究匿名用户发表于 2026年05月06日 20:1616阅读
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1. MPC基础框架与跨领域应用发展脉络

1.1 MPC核心原理与技术特征

模型预测控制（Model Predictive Control, MPC）作为一种先进控制策略，其核心在于通过显式地利用系统模型来预测未来的动态行为，并在此基础上优化当前的控制输入。MPC的逻辑架构主要由预测建模、滚动优化和反馈校正三大核心模块构成 1。

预测建模（Prediction Model）：MPC首先建立一个系统模型，该模型用于预测系统在未来一段时间内（预测时域）的状态和输出。这个模型可以是线性的或非线性的，取决于被控对象的复杂程度和对控制精度的要求。通过这个预测模型，MPC能够预见控制动作对系统未来轨迹的影响，从而在控制决策时充分考虑动态过程 123。

滚动优化（Rolling Optimization）：在每个控制周期，MPC会根据当前系统状态、预测模型以及设定的性能指标（如跟踪误差最小化、能耗最低、舒适度最大等）和操作约束（如执行器饱和、安全边界、能耗限制等），在线求解一个开环优化问题。这个优化问题通常在有限的预测时域内进行，目标是计算出一系列最优的未来控制输入。优化过程会考虑到多种约束条件，包括输入约束、输出约束和状态约束，确保系统运行在安全和经济的范围内。这种能力使得MPC在处理复杂系统和多变量耦合问题时具有显著优势 1245。

反馈校正（Feedback Correction）：MPC的“滚动”或“移动时域”特性体现在，在每个控制周期内，优化问题被求解后，只有计算出的第一个控制输入被实际施加到系统中。在下一个控制周期，系统会测量到新的当前状态，并将其作为新的初始条件，重新进行预测和优化。这种反馈机制能够有效地补偿模型误差、外部扰动以及未建模动态的影响，增强了系统的鲁棒性和适应性 4678。

相较于传统的反馈控制方法，如PID控制，MPC在多约束适配和多目标优化层面展现出差异化优势。PID控制器通常难以直接处理复杂的系统约束，需要额外的限幅或抗积分饱和措施，且其参数整定往往针对单一目标进行。而MPC通过在优化问题中显式地包含各种硬约束（如执行器极限、安全阈值）和软约束（如舒适度、经济性），能够确保控制系统始终在允许的操作范围内运行，并能够通过权重调整实现多个性能目标之间的权衡。此外，MPC的预测能力使其能够提前预判并应对未来可能出现的扰动或变化，从而在更高层次上实现系统性能的优化，尤其适用于具有显著延迟、多变量耦合或严格操作限制的复杂工业过程、自动驾驶和机器人系统 9101112131415161718。这种前瞻性和全局优化能力是MPC成为先进控制领域研究热点的重要原因。

1.2 三大领域MPC应用演进历程

模型预测控制（MPC）的应用演进是一个从工业过程控制发端，逐步扩展至自动驾驶和机器人等新兴领域的历程，其技术成熟度和应用深度在不同领域呈现出阶段性特征。

工业过程控制领域：早期成熟与持续深化

MPC在工业过程控制领域拥有悠久的历史和最广泛的工业应用基础 19。早在20世纪70年代末80年代初，MPC便开始应用于炼油、化工等流程工业，解决了传统控制方法难以处理的多变量、强耦合、大滞后和存在操作约束的复杂问题。

  • 早期阶段 (20世纪70年代末-90年代初)：MPC主要以线性模型为基础，应用于对稳态性能和约束满足有严格要求的流程工业。这一时期，MPC的核心突破在于能够将过程约束（如设备容量、产品质量规范、安全限值）直接纳入控制器设计，并通过在线优化来计算控制动作，显著提高了生产效率、产品收率和运行安全性。例如，在炼油厂中，MPC被用于优化分馏塔的操作，最大化高价值产品的产出同时避免超温超压等危险工况。
  • 发展阶段 (20世纪90年代中期-21世纪初)：随着计算能力的提升，非线性MPC（NMPC）开始受到关注，以更好地处理实际工业过程中的非线性动态 20。同时，鲁棒MPC、自适应MPC等技术被引入，以应对模型不确定性和外部扰动。分布式MPC和分层MPC结构也开始应用于大型、复杂的工业系统，实现子系统间的协调控制。这一时期，MPC成为许多大型石化、电力、冶金企业优化运行的关键技术之一。
  • 近期与未来 (21世纪10年代至今)：MPC在工业领域的应用进一步深化，例如，实时优化（RTO）策略相关研究仍在持续进行 21。同时，数据驱动的建模方法、机器学习与MPC的结合成为新的研究热点，例如灰箱建模（grey-box modeling）方法被用于在线监测和预测批次生产过程中的产品质量 22。MPC也开始在离散制造、半导体制造（如基于种群平衡方程模型的粒子分布控制 23）等领域展现潜力，并适应工业4.0和数字化转型的需求，支持更智能、柔性的生产模式。

自动驾驶领域：从轨迹跟踪到决策控制一体化

MPC在自动驾驶领域的应用历史相对较短，但发展迅速，是实现车辆高精度、安全、舒适控制的关键技术之一 24。

  • 早期阶段 (21世纪初-2010年左右)：MPC主要被用于解决自动驾驶车辆的底层控制问题，如路径跟踪。通过模型预测控制，能够优化控制动作，使车辆精确跟踪预设路径，并处理各种约束（如轮胎摩擦极限、转向角限制） 25。例如，基于改进MPC的路径跟踪控制器被提出，通过模糊自适应权重控制来平衡跟踪精度和车辆动态稳定性，提升驾驶舒适性 26。
  • 发展阶段 (2010年-2020年左右)：随着自动驾驶技术向更复杂场景演进，MPC开始扩展到更高级的决策和规划层面。融合了感知信息的决策控制一体化MPC成为研究重点，使车辆能够根据实时环境信息（如障碍物、其他车辆）进行路径规划和避碰。随机MPC（Randomized MPC）的实时实现，通过GPU加速和频率域采样技术，在自动驾驶的避碰任务中展现了优异的控制性能和计算速度 27。此外，事件触发的MPC算法也开始应用于复杂交通环境（如交叉路口）的车辆路径规划 28。
  • 近期与未来 (2020年至今)：MPC与人工智能、尤其是深度学习的结合日益紧密。利用LSTM-RNN等神经网络进行周围车辆运动预测，并将其融入MPC框架，提升了自动驾驶车辆在复杂多车道转弯路口的规划安全性 29。同时，为了确保自动驾驶系统的安全性，MPC也被用于设计预测安全滤波器，即使在学习型控制策略可能不安全的情况下，也能保证车辆不偏离车道边界 30。MPC在自动驾驶中的应用正朝着更高级别的自主性、更强的环境适应性和更高的安全性方向发展。

机器人领域：从单体控制到全身协调与多智能体协作

MPC在机器人领域的应用是近十年来的一个活跃研究方向，尤其在足式机器人和人形机器人等高动态、高自由度系统控制中展现出巨大潜力 31。

  • 早期阶段 (21世纪初-2010年左右)：MPC在机器人领域的应用主要集中在工业机器人手臂的轨迹跟踪和移动机器人的路径规划。由于机器人动力学的复杂性，早期的MPC应用多采用简化模型，以降低计算复杂度，实现实时控制。例如，MPC被用于优化机器人运动，使其在满足关节力矩、速度、位置等约束的同时，完成指定任务。
  • 发展阶段 (2010年-2020年左右)：随着计算能力的飞跃和优化算法的进步，MPC开始应用于更复杂的机器人系统，如足式机器人和人形机器人。这一时期，基于简化模型的MPC（如质心动力学模型）被广泛用于生成机器人的步态和全身运动轨迹，并通过分层控制结构将MPC规划的高层运动指令传递给低层关节控制器 31。同时，学习型控制（Learning-based Control）与MPC的结合也开始出现，以提升机器人在未知环境下的适应性和性能 32。
  • 近期与未来 (2020年至今)：全身控制MPC成为人形机器人和复杂多关节机器人研究的热点，它能够协调机器人所有关节和末端执行器的运动，实现平衡、操纵和导航等复杂任务。多智能体协同MPC在多机器人系统中的应用也逐渐增多，例如，通过学习交互感知轨迹预测模型，实现去中心化的多机器人运动规划和避碰，无需实时通信即可达到接近中心化规划的性能 33。此外，为了应对机器人系统在现实世界部署中的安全挑战，结合MPC的预测安全框架和安全强化学习（Safe Reinforcement Learning）等技术也正在兴起 34。机器人领域的MPC正向着高动态、强鲁棒、自适应和安全协同的方向快速演进。

2. 三大领域MPC核心技术路线与代表性研究成果

2.1 自动驾驶领域MPC技术路线

自动驾驶作为MPC应用的前沿阵地，其技术路线随着车辆智能化水平的提升而不断演进。主要的核心技术路径包括轨迹跟踪MPC、决策控制一体化MPC以及多智能体协同MPC。

2.1.1 轨迹跟踪MPC

轨迹跟踪MPC是自动驾驶领域MPC最基础也是最广泛的应用之一。其核心目标是使车辆精确地跟随预设的参考轨迹，同时满足车辆动力学约束和路面附着条件。这一技术通常采用车辆动力学模型作为预测模型，并通过在线优化来计算最优转向角和加速度，以最小化跟踪误差并确保车辆稳定性。

  • 线性时变MPC (LTV-MPC)：考虑到车辆在不同速度和工况下动力学特性会发生变化，线性时变模型预测控制器（LTV-MPC）被广泛应用于轨迹跟踪。它在每个控制周期内将非线性车辆模型线性化，形成一个时变线性系统，然后进行二次规划求解。例如，Cao等 35 针对自动驾驶车辆的轨迹跟踪控制，提出了一种考虑转弯特性的LTV-MPC控制器。该控制器通过简化车辆动力学模型和轮胎模型，并优化LTV-MPC设计，在CarSim和MATLAB/Simulink联合仿真中验证了其在复杂严苛工况下（如双移线轨迹、不同车速和路面附着条件）的自适应性，显著提升了轨迹跟踪精度和实时性能，有效避免了车辆侧滑或偏离轨迹的情况 35。Pang等 36 也提出了一种LTV-MPC方法，通过对非线性跟踪误差模型进行连续线性化，形成了二次规划优化问题，在实现高精度轨迹跟踪的同时，降低了计算成本，并通过仿真和实验验证了其在各种驾驶条件下对预设参考路径的精确性和稳定性。
  • 自适应权重MPC：为了平衡跟踪精度、驾驶舒适性和车辆稳定性，研究人员尝试通过自适应调整MPC成本函数中的权重来优化控制器性能。Wang等 26 提出了一种基于模糊自适应权重控制的改进MPC控制器，用于解决自动驾驶车辆在路径跟踪过程中可能出现的舒适性问题。该控制器在确保跟踪精度的同时，考虑了车辆的动态稳定性，并通过模糊自适应控制算法动态调整MPC成本函数的权重。与纯追踪控制器和经典MPC控制器相比，该方法在CarSim-Matlab/Simulink联合仿真中表现出更好的跟踪性能和转向平稳性 26。Lim等 37 提出了一种自动权重调整方法，该方法通过粒子群优化算法，根据驾驶数据自动调整MPC的权重因子，从而实现个性化的跟车控制。这有助于减少工程师寻找最优权重因子所需的工作量和时间 37。
  • 耦合效应与状态不确定性处理：在实际驾驶中，车辆的横向和纵向运动往往存在耦合效应，且车辆状态参数难以精确测量。Yuan等 38 提出了一种基于LQR-MPC的轨迹跟踪控制器，用于处理自动驾驶车辆的横纵向耦合效应和驾驶状态不确定性。该分层控制器在上层采用LQR计算期望前轮转向角以最小化横向跟踪偏差，同时采用MPC计算期望加速度以维持规划车速。下层控制器则通过相应部件实现期望的转向角和加速度。此外，该研究还引入了基于扩展卡尔曼滤波器（EKF）的观测器来更新难以直接测量的车辆驾驶状态。CarSim-MATLAB/Simulink联合仿真结果表明，该耦合控制器能够鲁棒地实现轨迹跟踪，并有效降低横向跟踪误差 38。

2.1.2 决策控制一体化MPC

随着自动驾驶系统复杂度的增加，将决策（如路径规划、行为决策）与底层控制（如轨迹跟踪）分离的设计方法，往往难以在复杂动态环境中取得全局最优。决策控制一体化MPC旨在将这两个层面融合，使MPC能够直接根据环境感知信息进行高层次决策并输出底层控制指令。

  • 随机MPC (Randomized MPC)：为解决实时计算复杂性和在动态环境中的决策问题，随机MPC被提出。Muraleedharan等 27 针对自动驾驶的碰撞避免任务，在RC模型车上成功实现了随机MPC的实时部署。该研究讨论了频率域采样技术以避免不必要的随机性，并利用GPU加速计算，显著提升了计算速度和控制性能。实验结果表明，该方法在碰撞避免任务中表现出良好的效果 27。
  • 行为预测融合MPC：为了在复杂交通流中实现安全、平稳的驾驶，融合对其他交通参与者行为的预测至关重要。Chen等 39 提出了一种以人为中心的轨迹跟踪控制策略，将驾驶员切入行为预测融入MPC。该研究使用带有LSTM单元的循环神经网络（RNN）来预测切入车辆的驾驶员行为，然后将这些预测集成到MPC控制器中以跟踪参考轨迹。通过在驾驶模拟器上进行的测试以及CarSim仿真，验证了该控制器在不同驾驶情景下与切入车辆协同合作的能力，并能产生平滑的过渡过程 39。
  • 驾驶风格融合MPC：为了提高用户对自动驾驶系统的接受度，将人类驾驶员的驾驶风格融入MPC设计成为一个重要方向。Li等 40 提出了一种结合轨迹规划和跟踪的算法，通过人工势场（APF）方法建模交通环境和驾驶风格，并将这些APF值集成到MPC设计过程中，从而优化轨迹和控制输出。仿真实验表明，该控制器能够反映不同驾驶风格（如谨慎型和激进型），并在跟车和变道场景中有效运作 40。
  • 深度强化学习与MPC融合：近年来，深度强化学习（DRL）在复杂决策任务中展现出强大能力 41。将DRL与MPC结合，可以利用DRL的决策能力和MPC的精确控制与约束处理能力。Wan等 42 针对高速公路上的自动驾驶车辆编队变道问题，提出了一个基于多智能体深度确定性策略梯度（MA-DDPG）和自适应MPC（AMPC）的编队变道跟踪控制框架。该框架使用MA-DDPG实现纵向跟车控制，处理非线性系统和连续状态空间，并通过AMPC结合五次多项式曲线完成横向控制，并引入模糊控制器补偿前轮转向角。CarSim/Simulink联合仿真结果表明，该框架在不同车速下均能有效跟踪，并使纵向速度曲线平滑 42。

2.1.3 多智能体协同MPC

在多车系统（如车队、交叉口交通）中，为了实现高效、安全的协同行为，多智能体协同MPC成为关键技术。它允许每个智能体在考虑自身约束的同时，与其他智能体进行协调，以实现共同目标。

  • 合作路径跟踪：Hung等 43 提出了一种多车辆合作路径跟踪（CPF）解决方案，明确考虑了车辆输入约束和车际通信网络的拓扑结构。该方案将CPF问题解耦为单车受限路径跟踪和多智能体系统（MAS）协调两个子问题。前者通过采样数据MPC方案解决，后者通过带有事件触发通信（ETC）机制的分布式控制律解决。仿真实例表明，该CPF策略能够实现稳定闭环，使得每个车辆的路径跟踪误差全局渐近稳定，并且车辆之间的协调误差有界 43。
  • 安全与协调：Schwarting等 44 的综述强调了在复杂、拥挤的环境中，自动驾驶车辆需要能够提供安全且符合系统性能的规划方法，同时建模与其他交通参与者交互的不确定性。该文指出，MPC在此类场景下能够通过显式处理安全约束和预测其他智能体行为，实现多智能体之间的安全协调。此外，结合学习技术（如交互感知规划和行为感知规划）可以进一步提升多智能体MPC的性能 44。
  • 能量管理与成本优化：Hu等 45 提出了燃料电池/电池混合动力电动汽车的成本最优预测能量管理策略，首次建立了模型预测控制框架，以最小化包括氢气成本以及燃料电池和电池退化成本在内的总运行成本。这一研究的预测控制框架和成本优化思想，对于需要考虑多目标和约束的分布式多智能体系统协同优化具有借鉴意义。

2.2 机器人领域MPC技术路线

在机器人领域，模型预测控制（MPC）因其处理复杂动态、多约束以及在线优化的能力，成为从移动机器人到高度复杂的人形机器人控制的核心技术之一。本节将聚焦移动机器人路径规划MPC、协作机器人力位混合控制MPC以及人形机器人全身控制MPC等主要方向，总结其技术创新思路与代表性研究成果。

2.2.1 移动机器人路径规划MPC

移动机器人（包括轮式、足式等）的路径规划和跟踪是其自主导航的基础。MPC在此类应用中，不仅要考虑机器人的运动学和动力学约束，还需要实时避障、应对环境不确定性，并优化路径效率或能耗。

  • 全向移动机器人路径规划与控制：Liu等 46 提出了一种结合势场法（Potential Field Method）的全向移动机器人MPC控制和路径规划方法。该方法利用势场来引导机器人在环境中运动并规避障碍物，同时MPC负责实时调整控制输入以精确跟踪规划的路径并满足运动约束。这种结合使得机器人在复杂环境中既能实现高效规划，又能保证精确控制。
  • 非完整移动机器人的轨迹跟踪：非完整机器人（如大多数轮式移动机器人）由于其运动学约束（例如不能横向平移），轨迹跟踪极具挑战性。Nascimento等 47 对非完整移动机器人的轨迹跟踪MPC进行了综述，指出MPC能比经典控制方法取得更好的效果。该综述回顾了MPC在该领域的问题表述和方法，并强调了近年来的突破，为研究人员提供了进入该领域的起点。Li等 48 提出了一种用于4WIS（四轮独立转向）机器人高速轨迹跟踪的MPC方法，并通过仿真验证了其在高速、受限场景下的有效性。另一项研究也指出，通过MPC控制输入，可以使轮式移动机器人在有滑移的情况下，实现参考路径的跟随，并适应滑移变化，为未来结合机器学习技术进行多地形导航提供了可能 49。
  • 避障与局部路径规划：为使移动机器人在动态环境中安全运行，避障是路径规划的关键环节。Li等 50 提出了一种结合人工势场（APF）和MPC的方法，用于移动机器人的轨迹跟踪和避障。APF用于局部路径规划，生成虚拟目标以引导机器人避开障碍物，MPC则用于跟踪此虚拟目标生成的路径。该方法通过仿真验证了其在单障碍物环境中的有效性。Yang等 51 提出了一种用于磁性微型机器人自主导航的框架，其中包含了一个双回路运动控制器。该控制器包括一个扰动观测器、一个模糊逻辑修正器和一个模型预测控制器，使微型机器人能够精确跟踪计算路径并智能避开碰撞。
  • 多机器人协同避障：在多机器人系统中，MPC也被用于解决分散式碰撞避免问题。Raibail等 52 的综述指出，MPC是处理多机器人碰撞避免的常用方法之一，尤其是在分散式方法中，因为它计算成本较低。该综述比较了包括MPC在内的不同碰撞避免策略，并讨论了它们在安全性和路径规划上的侧重。

2.2.2 协作机器人力位混合控制MPC

协作机器人需要安全、高效地与人类或环境进行交互。力位混合控制是实现这一目标的关键，而MPC由于能够显式处理交互力和运动约束，成为其理想的控制策略。

  • 柔顺控制与力交互：Piccinelli和Muradore 53 提出了一种用于位置控制机械手的线性MPC方法，以保证与未知环境的安全交互力。该方法通过将交互力作为约束集成到MPC中，同时建模了环境和机器人动力学。实验结果表明，该带有力约束的MPC控制器在UR5e协作机器人上成功进行了抛光任务验证，证明了其在安全关键场景中控制交互力的能力。
  • 混合执行器控制：Rouzbeh和Bone 54 研究了混合气动-电动线性执行器（HPEA）的位置控制和力分配算法。他们发现，由于HPEA结合了气动执行器的大力/低带宽特性和电动执行器的高带宽/小力特性，MPC方法能通过智能分配所需的力（或扭矩）显著改善HPEA的性能。与传统线性控制器相比，MPC在位置跟踪和力分配方面表现更优，并能实时计算。
  • 康复外骨骼机器人控制：MPC也被应用于康复外骨骼机器人。Mashud等 55 在对康复外骨骼机器人控制技术的系统综述中提到，MPC能够提供基于优化的解决方案，以实现精确、适应性强的运动辅助和安全的人机交互。

2.2.3 人形机器人全身控制MPC

人形机器人具有高自由度和复杂的动力学特性，实现其动态、平衡的全身运动是一个巨大的挑战。MPC能够协调全身关节运动，同时满足平衡、接触力和关节限制等复杂约束，是实现类人行为的关键技术。

  • 动态步态生成与全身运动规划：Katayama等 31 对足式和人形机器人MPC进行了综述，强调了其在过去十年中的活跃发展。该综述从动力学模型、算法和应用三个方面，详细阐述了MPC如何从基于简化模型的控制发展到基于全身模型的控制，实现更复杂、更动态的运动。Meduri等 56 提出了一个名为BiConMP的非线性MPC框架，用于足式机器人的全身运动规划。该框架通过高效利用机器人动力学结构，实现在线生成全身轨迹。BiConMP成功应用于实际四足机器人，生成了各种循环步态，并在不同地形、应对意外推力以及在线切换步态时表现出色。它还在模拟中生成了人形机器人和另一款四足机器人的动态运动。
  • 实时全身优化控制：全身MPC面临的主要挑战之一是巨大的计算负担，这限制了其在实时高频控制中的应用。Ishihara等 57 开发了一个多时间尺度控制框架，结合了计算效率高的分层MPC和生物启发式控制器，以实现人形机器人的全身优化控制。该框架能够在短时间内更新全身运动，并在滑冰任务中，包括模拟和真实机器人，生成了各种敏捷动作，如跳过障碍和从悬崖翻下。Dantec等 58 探讨了通过一阶近似MPC解来应对高频反馈的挑战，利用MPC优化问题中的线性状态反馈控制器（Riccati增益）作为低层控制回路的输入。他们提出，这种方法可以显著降低计算量，使全身控制在人形机器人上实现更高的反馈频率，并通过在Talos人形机器人上的实际实验证明了其有效性。
  • 多接触与重心高度变化规划：Mirjalili等 59 提出了一种新的全身MPC方案，用于人形机器人生成多种全身动作，包括外部接触力和重心（CoM）高度变化。该算法通过三阶段优化，即CoM垂直运动、关节角度和接触力规划，来自动计算外部接触的选择和时机。该方案在保持线性倒立摆模型（LIPM）简单性的同时，克服了其局限性，通过仿真和在人形机器人上的实验验证了其在多接触场景下生成各种全身动作的能力。
  • 非平坦地形自适应运动生成：Meng等 60 提出了一种自适应运动规划器，用于人形机器人在非平坦地形上的在线运动生成。该规划器结合了高效行为生成器（EBG）和非线性质心模型预测控制器（NC-MPC），其中EBG负责优化物理可行的全身模板行为并为NC-MPC提供可靠的暖启动，而NC-MPC则在线生成反应性运动以适应实际局部环境。该方法在仿真和真实人形机器人BHR7P上验证了其在非平坦地形上穿越的有效性。

这些研究共同描绘了MPC在机器人领域从基础路径规划到复杂全身协调，再到智能人机交互和动态环境适应的广阔应用图景。MPC凭借其固有的优化能力和对约束的显式处理，正不断推动机器人技术向更高智能、更强自主性和更安全交互的方向发展。

2.3 工业过程控制领域MPC技术路线

工业过程控制是模型预测控制（MPC）最初的摇篮，也是其应用最为广泛和成熟的领域。MPC在化工、石化、冶金、电力等流程工业中扮演着核心角色，解决了传统控制方法难以处理的复杂多变量、强耦合、大滞后和存在严格操作约束的问题。本节将重点梳理线性MPC、非线性MPC和分布式MPC在这些场景下的应用路线，并归纳核心代表性成果的技术价值与工业落地效果。

2.3.1 线性MPC在工业过程控制中的应用

线性模型预测控制（Linear Model Predictive Control, LMPC）是工业过程控制领域应用最广泛的MPC形式。其核心在于使用线性系统模型来预测过程行为，并通过求解二次规划（Quadratic Programming, QP）问题来获得最优控制输入。LMPC的普及得益于其相对较低的计算复杂度和在许多工业过程中良好的控制性能，尤其是在过程操作点附近行为可被线性近似的场景。

  • 数学表述与优势：LMPC通常基于状态空间模型或输入输出模型（如ARX、FIR模型）进行预测。在每个控制周期，它通过最小化一个二次目标函数来计算未来控制序列，该目标函数通常包括跟踪误差和控制输入的加权平方和。同时，将系统的操作约束（如阀门开度限制、温度、压力、浓度上限等）直接纳入到QP问题的约束条件中。这种显式处理约束的能力是LMPC相对于传统PID控制器的显著优势，能够确保系统在安全、经济的范围内运行，并有效应对多变量耦合问题，提高操作效率和产品质量 6162。
  • 化工与石化工业的基石：LMPC在炼油厂和石化工厂中发挥着不可替代的作用。例如，分馏塔、反应器、换热网络等关键设备的优化控制。LMPC能够有效地在生产过程中平衡产量、产品质量、能耗和安全性等多重目标。它可以通过预测未来扰动（如进料组成或流量变化），提前调整操作变量，从而减少产品质量波动，提高收率，并降低能耗。Martin等在水泥行业的应用案例中提到，MPC在窑炉/冷却器应用中，能够比典型的人工干预快三倍地从涂层脱落等重大事故中恢复，显著提升了生产的稳定性和效率 63。此外，MPC也被应用于石化供应链规划中，以应对不确定性并优化多周期、多产品的规划问题 64。
  • 电力系统与微电网：在智能电网和微电网领域，LMPC被广泛用于优化能源管理和电力调度。例如，Morstyn等提出了一种凸LMPC策略，用于分布式交流微电网中电池储能系统之间的动态优化潮流。该策略通过线性化电压-电流模型和功率潮流近似，将优化问题转化为凸优化，从而实现快速鲁棒求解，比非凸优化方法计算时间减少1000倍，使其适用于实时MPC实施 65。Olivares等设计了一个集中式能源管理系统（EMS），利用MPC技术来优化孤岛微电网的运行，通过分解机组组合（UC）和最优潮流（OPF）问题，避免了混合整数非线性公式，并有效地调度了储能单元，验证了三相模型在电压限制和无功功率支持方面的重要性 66。Mahdavi等则利用LMPC来控制分布式空调负荷，以补偿太阳能发电的波动，这表明LMPC在需求侧管理和电网平衡方面的潜力 67。
  • 其他工业应用：LMPC也在其他工业领域展现出价值。例如，在造纸工业中，LMPC被用于控制纸张的厚度和湿度，确保产品质量。在采矿冶金行业，如水泥生产，LMPC用于优化磨机性能，处理其固有的非线性行为，通过神经网络模型实时调整控制器增益，显著改善了设定点跟踪和扰动抑制能力 63。此外，模型预测控制（MPC）的相关识别方法已被用于为Hammerstein模型获取非线性模型，这对于解决诸如湿法制粒等具有非线性动态特性的过程控制问题具有重要意义 6869。

总体而言，线性MPC凭借其成熟的理论基础、高效的在线求解能力和对约束的显式处理，在工业过程控制中占据主导地位。它不仅提升了生产过程的自动化水平和经济效益，也为应对日益复杂和严格的工业操作要求提供了强有力的工具。

2.3.2 非线性MPC在工业过程控制中的应用

虽然线性MPC在许多工业过程中表现良好，但当过程具有显著的非线性特性、宽广的操作范围或严格的性能要求时，线性模型往往不足以准确描述系统行为，这使得非线性模型预测控制（Nonlinear Model Predictive Control, NMPC）成为更优的选择 3。NMPC通过直接使用非线性系统模型进行预测和优化，能够更精确地捕捉过程的动态特性，从而在更广的操作范围内实现更好的控制性能和经济效益。

  • 技术优势与挑战：NMPC的核心优势在于其能够显式地处理强非线性动力学以及非凸的约束条件，从而在整个操作区域内获得更优的控制性能 3。这对于那些在不同工况下表现出截然不同行为的复杂工业过程尤为重要。然而，NMPC的主要挑战在于其求解优化问题的计算复杂度远高于LMPC。非线性优化问题通常需要迭代求解，且可能存在多个局部最优解，导致求解时间长，难以满足实时性要求。此外，非线性模型的辨识和验证也更加复杂。
  • 化工反应器：化工反应器是典型的非线性过程，其反应速率常数通常随温度呈指数关系变化。NMPC能够有效地控制这些反应器，使其在最佳产率和选择性下运行，同时避免温度失控等安全问题。Piche等 70 提出了一种基于神经网络的非线性动态模型构建技术，用于NMPC算法，成功应用于聚乙烯反应器和连续搅拌釜式反应器（CSTR）等非线性工业过程，验证了其在炼油、石化、纸浆和造纸、电力和食品等多个工业应用中的有效性。他们的研究表明，神经网络模型能够从经验数据中学习复杂非线性，并有效地集成到NMPC框架中。Wu等 71 进一步探讨了利用循环神经网络（RNN）集成来预测非线性动力学的NMPC设计，旨在改善预测精度和闭环性能，同时利用并行计算减少计算时间，并在化学反应器示例中展示了其潜力。
  • 精馏塔：精馏塔是化工过程中常见的非线性多变量分离设备。其产品纯度、塔釜液位、回流比等变量之间存在复杂的非线性耦合。NMPC可以优化精馏塔的操作，最大化高价值产品的产出，同时最小化能耗。例如，Zhang等 72 提出了一种将神经网络模型与第一性原理模型相结合的方法，用于实时优化（RTO）和MPC，并应用于CSTR和精馏塔的例子。在精馏塔的案例中，前馈神经网络被用来获取相平衡性质，并与第一性原理模型结合在RTO中，以最大化操作利润，验证了该方法在提升工业操作利润方面的有效性。
  • 生物发酵过程：生物发酵过程通常涉及复杂的微生物动力学、底物消耗、产物生成和热力学平衡，这些都呈现出强烈的非线性。NMPC在生物发酵中的应用能够优化生产策略，提高目标产物的产量和质量。通过实时调整底物进料速率、温度、pH值等，NMPC可以引导发酵过程沿着最佳路径进行，同时处理过程中的不确定性和扰动。
  • 其他复杂过程：NMPC还广泛应用于其他具有强非线性特征的工业过程，如生物质气化、高炉炼铁、聚合物生产等。例如，Peng等 73 利用高斯径向基函数（RBF）神经网络的局部线性化ARX模型来描述一类光滑非线性非平稳工业过程的动态，并将其应用于火电厂氮氧化物分解（de-NOx）过程的NMPC设计。实验证明了所提出的NMPC设计的可行性、有效性以及在性能上的显著改进。
  • 经济型NMPC (Economic NMPC, EMPC)：近年来，经济型NMPC成为工业过程控制的一个重要趋势，旨在直接优化与经济效益相关的性能指标，而非仅仅稳定在设定点。Heidarinejad等 74 开发了经济型MPC设计，能够针对广泛的非线性过程系统，优化与一般经济考量相关的闭环性能，并在化学过程示例中评估了其性能和鲁棒性。Faulwasser等 75 的专著则提供了经济型非线性模型预测控制的全面概述，探讨了在稳定性与最优性方面的不同方法，包括带有或不带末端约束、以及基于耗散性和Lyapunov的方法。这些研究表明NMPC在提升工业生产的经济性方面具有巨大潜力。
  • 软件工具：为促进NMPC在工业界的普及，开发易于使用的NMPC软件工具也至关重要。Fiedler等 76 介绍了开源软件do-mpc，旨在解决NMPC推广面临的障碍，如模型不可用性、部署复杂性、缺乏快速原型工具以及可复用性差等问题。do-mpc通过与神经网络工具箱的互操作性简化了非线性系统辨识，通过OPC UA通信协议实现部署，并提供可复现的数据采样框架进行透明的控制器验证和系统辨识。

2.3.3 分布式MPC在工业过程控制中的应用

随着工业过程规模的不断扩大和复杂性的增加，集中式模型预测控制（Centralized Model Predictive Control, CMPC）面临着巨大的挑战。大型工业过程往往包含多个相互关联的子系统，如果采用CMPC，需要建立一个涵盖所有子系统行为的全局模型，并求解一个维度极高的优化问题，这不仅计算复杂度高、难以实现实时性，而且在模型建立、维护和故障诊断方面也存在困难。为了克服这些挑战，分布式模型预测控制（Distributed Model Predictive Control, DMPC）应运而生。DMPC将整个系统分解为多个相互协作的子系统，每个子系统都有一个局部控制器，负责控制其自身的部分，并通过有限的信息交换实现子系统之间的协调，以达到全局最优或接近最优的控制目标 77。

  • 技术原理与优势：DMPC的核心思想是将一个大规模的集中式优化问题分解为一系列规模较小的子问题，每个子问题由一个局部控制器独立求解。子控制器之间通过通信网络交换必要的信息（如预测轨迹、控制指令或协调变量）来实现协同作用，从而使整个系统作为一个整体来运行。这种方法不仅显著降低了每个控制器的计算负担，提高了实时性，而且增强了系统的模块化、可扩展性和鲁棒性。即使某个子系统发生故障，其他子系统仍能继续运行，提高了系统的容错能力。DMPC对于工业控制系统而言，通常用于控制具有多变量耦合的大规模过程 78。此外，当存在异步和延迟的测量反馈时，DMPC也能够有效处理 79。
  • 化工过程的复杂协调：化工过程，特别是大型一体化化工园区，通常包含多个相互连接的反应器、分离单元和换热网络，这些单元之间存在强烈的物料和能量耦合。DMPC在此类场景下展现出独特的优势。例如，针对非线性系统中的异步、延迟测量反馈问题，有研究设计了迭代式DMPC方案，并成功应用于苯催化烷基化过程的例子中，证明了其能够保证闭环系统状态的最终有界性 79。在多智能体共识问题中，DMPC也被提出用于解决分布式输出反馈控制问题 80。对于具有耦合特性的工业过程，研究者提出了基于协调的网络化分布式模型预测控制（NDMPC）策略，以补偿子系统间通信时变延迟，并通过一个由两个单元连接的整体工厂案例验证了其有效性 78。进一步地，有研究提出了如何将集中的MPC和分布式的MPC结合起来，以利用各自的优势 81。研究表明，问题参数（如状态测量和设定点）会显著影响集中式最优控制问题的计算成本或求解时间。DMPC在计算成本高时更受欢迎，而CMPC在成本低时更有效。通过机器学习分类器可以识别何时适合使用哪种策略，并在控制的移动时域中策略性地选择CMPC或DMPC，从而提高了过程控制的整体质量 81。
  • 冶金工业的流程优化：在冶金工业中，如钢铁生产中的烧结、炼铁、炼钢、轧钢等环节，过程复杂且相互影响。DMPC可以用于协调不同工序之间的生产节奏和物料流，优化整体生产效率和产品质量。例如，在焦化厂的优化运行中，DMPC能够协调不同焦炉的生产计划，以满足高炉对焦炭的需求，同时优化能源消耗。在铁去除系统中，研究者提出了基于离线强化学习的最优控制算法，以克服复杂反应机制、不确定性以及互连反应器带来的控制难题，展示了其在实际工业褐铁矿除铁过程中的有效性和灵活性，该算法可以视为一种分布式思想的体现 82。
  • 离散制造与能源管理：在离散制造领域，DMPC可用于协同多个生产线或机器人单元，实现柔性制造和智能调度。例如，在大型商业建筑的温度调节中，为了最小化能源成本，传统的集中式控制系统不切实际。Patel等提出了一种分布式控制系统，通过分解策略考虑了热能存储、区域交互和冷却器设备，并使其在计算上易于处理，从而有效地将低层空侧问题解耦并分布式求解，这使得它易于扩展到大型应用 83。此外，DMPC也被应用于工厂范围内的经济优化，特别是在结合批量和连续单元的过程工业中，如甜菜糖厂的能效优化，通过分层架构实现批量单元的非集中式优化和连续单元的平滑集成 84。
  • 与其他技术的融合：DMPC不仅独立发展，还与其他先进技术融合，进一步提升其在工业应用中的性能。例如，将模糊逻辑引入DMPC，以实现代理之间的模糊协商，实现无偏差分布式预测控制，这在实验性的四罐系统中得到了验证，即使在子系统耦合和系统模型不匹配的情况下也表现出有效性 85。此外，工业物联网（IIoT）和工业网络物理系统（ICPS）的兴起为DMPC提供了新的机遇，但也带来了网络延迟、数据丢包等挑战。针对这些问题，有研究对工业CPS的模型基分布式控制和滤波进行了综述，特别关注传感器网络、机械臂和电力系统，并提出了未来研究的挑战 77。大型工业过程的自动分解工具也正在开发，以简化DMPC在平台上的应用 86。
  • 未来展望：尽管DMPC在工业过程控制中取得了显著进展，但仍面临一些挑战，例如子系统分解策略的通用性、通信网络不稳定性的影响、安全性与隐私性保障以及与更高层决策系统（如企业资源规划ERPI）的无缝集成等。未来的研究将继续探索更高效的协调机制、更鲁棒的算法设计以及更智能的自适应分解方法，以进一步拓展DMPC在工业4.0背景下的应用深度和广度。

分布式MPC凭借其在处理大规模、复杂工业系统方面的独特优势，已经成为推动工业自动化和智能化升级的关键技术之一。它不仅提高了生产效率和经济效益，也为实现更安全、更可靠的工业运行提供了强有力的保障。

3. MPC实时优化技术研究进展

模型预测控制（MPC）的实时性是其在自动驾驶、机器人和高速工业过程控制等动态应用中面临的关键挑战。为了在每个采样周期内快速求解优化问题并输出控制指令，研究人员在MPC的实时优化技术方面进行了大量探索。本节将深入探讨低复杂度求解算法优化、端边架构适配的MPC轻量化设计以及数据驱动融合的MPC求解加速等主要研究进展。

3.1 低复杂度求解算法优化

MPC的核心在于在线求解一个带有约束的优化问题，其计算复杂度往往是限制其实时应用的主要因素。因此，开发高效、低复杂度的求解算法是实现MPC广泛应用的关键。主要的优化方向包括快速二次规划（QP）求解器、显式MPC以及基于算子拆分（Operator Splitting）的方法。

3.1.1 快速二次规划（QP）求解器

在许多MPC应用中，特别是当系统模型为线性且目标函数为二次时，需要求解一系列二次规划（QP）问题。QP求解的效率直接决定了MPC的实时性能。

  • 内点法（Interior Point Methods）：内点法是一种解决凸优化问题的有效方法，以其良好的数值稳定性和多项式时间复杂度而闻名。针对MPC中出现的凸多阶段问题，研究人员设计了高效的内点法。例如，Domahidi等 87 提出了一种专门针对凸多阶段问题的内点法，能够处理大多数线性动力学MPC问题，包括二次约束。他们的研究详细说明了实现高速和卓越数值稳定性的算法细节，并指出通过低秩矩阵前向替换方案可以减少某些二次或线性约束的计算负担。与现有最快的MPC求解器相比，他们的求解器在速度上快2-5倍，代码大小减少3-70倍，并且对于大型问题和带二次约束的QP问题表现出高效性，使得MPC能够在低成本嵌入式硬件上实现 87。
  • 主动集法（Active Set Methods）：主动集法也是解决QP问题的经典方法之一。它通过迭代地确定活跃约束集来寻找最优解。Milman和Davidson 88 提出了一种新的非可行主动集方法，用于解决MPC中出现的QP优化问题。该方法在六个具有代表性的工业控制系统示例中，比传统的活跃集方法快10倍，甚至比原对偶内点法更快 88。Ferreau等 89 提出了一种在线主动集策略，利用前一个QP解的信息来加速当前QP的求解，尤其适用于活跃约束集变化不大的情况。他们还提出了CPU时间受限的修改版本，使其适用于严格的实时应用。在一个包含240个变量和1191个不等式的挑战性测试示例中，该策略将QP的CPU时间降低到100毫秒以下，比标准主动集QP求解器快约一个数量级 89。
  • 定制化与结构利用：针对MPC问题的特殊结构进行定制化设计是提升QP求解速度的有效途径。Wang和Boyd 90 描述了一系列通过在线优化来提高MPC速度的方法。这些定制方法利用了MPC问题的特定结构，能够比使用通用优化器快约100倍地计算控制动作。例如，对于一个包含12个状态、3个控制变量、预测时域为30个时间步的问题（需要解决一个包含450个变量和1284个约束的QP），他们的算法可以在大约5毫秒内计算出控制动作，从而使MPC能够以200Hz的频率运行 90。Mattingley等 91 强调了代码生成技术在MPC中的应用，通过将高层语言中的RHC策略自动转换为定制求解器的源代码。这种定制求解器通常比通用求解器快几个数量级，在标准处理器上能在毫秒或微秒级别内求解，使得RHC策略能够以千赫兹的速率运行 91。Frison等 92 结合高性能计算技术和MPC定制求解器，并利用目标架构的特定指令集，使得其开发的HPMPC求解器比现有最先进的求解器快2到8倍，并且在几百个状态的MPC问题中仍能保持高性能 92。

3.1.2 显式MPC（Explicit MPC）

显式MPC（eMPC）是另一种显著降低在线计算负担的方法。其核心思想是将MPC问题视为一个参数化规划问题，在离线阶段预先计算出所有可能状态下的最优控制律，并将其存储为分段仿射函数的形式。在线阶段，控制器只需根据当前状态进行查表和简单的函数评估，而无需进行复杂的优化计算。

  • 原理与优势：对于线性MPC问题，当系统模型是线性的，成本函数是二次的，并且约束是多面体时，最优控制律是状态的分段仿射函数。这意味着控制空间可以划分为一系列被称为“临界区域”的多面体区域，每个区域内对应一个仿射控制律。在线运行时，控制器只需确定当前状态位于哪个临界区域，然后应用相应的仿射控制律。这种方法将复杂的在线优化问题转化为简单的几何搜索和矩阵乘法，极大地降低了在线计算负担，使其适用于高速、低功耗的嵌入式系统 9394。
  • 挑战与局限性：显式MPC的主要挑战在于离线计算的复杂性和结果存储的需求。随着状态维数、输入维数、预测时域和约束数量的增加，临界区域的数量会呈指数级增长，导致离线计算时间过长以及需要巨大的存储空间。这限制了显式MPC在处理大型或高维系统时的应用。
  • 优化与改进：为了克服存储和计算复杂性问题，研究人员提出了多种方法。例如，Isak Nielsen 95 提出了一种减少显式MPC所需内存的算法，旨在使mp-QP和显式MPC在嵌入式系统等内存受限的实际应用中更具可用性。该算法利用了QP问题在参数化解中的结构，以减少通用mp-QP解（特别是显式MPC解）的内存占用 95。

3.1.3 算子拆分方法（Operator Splitting Methods）

算子拆分方法是一类处理大规模优化问题的通用技术，它将复杂优化问题分解为一系列更简单、易于求解的子问题。这种方法在MPC中展现出巨大的潜力，尤其是在处理大型、分布式或非光滑约束问题时。

  • ADMM (Alternating Direction Method of Multipliers)：交替方向乘子法（ADMM）是目前最流行和有效的算子拆分方法之一。它通过分解目标函数和/或约束，将原始优化问题转换为若干个较小的子问题，并通过对偶变量进行协调。ADMM特别适用于分布式MPC，其中每个子系统控制器可以并行求解其局部问题，然后通过交换少量信息进行迭代协调。Stellato等 96 介绍了OSQP，这是一个基于算子拆分的二次规划求解器，其核心算法是ADMM，被设计用于高效解决大规模凸二次规划问题，并在MPC中得到广泛应用。
  • 应用与优势：算子拆分方法允许用户自定义数据结构和高度并行化，这使其非常适合在专用硬件（如FPGA）上实现。Shukla等 97 介绍了SPLIT，这是一个基于算子拆分方法的C代码生成工具，能够生成面向软件和硬件（CPU和FPGA）的C代码，以快速原型化优化算法。对于测试案例，硬件实现的加速比软件实现快3到11倍 97。Ferranti等 98 提出了一种使用算子拆分方法解决无限时域约束LQR问题（CLQR）的算法。他们将CLQR问题重新表述为没有终端约束的MPC问题，并将其分解为一系列固定维度的子问题，通过快速交替最小化算法求解。这种方法只需要求解无约束最小二乘问题和简单的梯度计算，显著降低了计算复杂性 98。Krupa等 99 提出了一个有效处理谐波MPC（HMPC）中二阶锥约束的方法，该方法通过算子拆分技术将计算时间与最先进的线性MPC求解器相媲美，使得HMPC及其求解器适用于嵌入式系统 99。
  • 多步预测控制中的应用：算子拆分方法还可以应用于多步MPC，以提高效率。Xie等 100 提出了一种快速QP求解器，用于多步预测电流控制。他们通过重新排列目标函数并预选两个接近参考导数的向量来显著减少搜索的切换状态数量，实验结果验证了该方法在保持良好控制性能的同时，计算时间较低 100。

总而言之，低复杂度求解算法的优化是MPC走向实时应用的核心驱动力。快速QP求解器（内点法、主动集法）、显式MPC以及基于算子拆分的ADMM方法等，通过不同的策略，有效降低了MPC在线优化的计算负担，使其能够在更快的采样速率和更复杂的场景中得到应用，极大地拓展了MPC的适用范围。

3.2 端边架构适配的MPC轻量化设计

随着物联网（IoT）、边缘计算和高动态应用（如自动驾驶、高速机器人）的兴起，将模型预测控制（MPC）部署到资源受限的边缘设备或嵌入式硬件上，以满足毫秒级甚至微秒级的求解需求，成为了一个重要的研究方向。传统的MPC算法往往需要强大的计算资源，难以直接在端边设备上高效运行。因此，针对端边架构进行MPC的轻量化设计，包括模型裁剪、并行计算优化以及硬件协同设计等方案，显得尤为关键。

3.2.1 MPC模型裁剪与简化

为了适应端边设备的计算能力限制，对MPC的预测模型进行裁剪和简化是常见的策略。

  • 降阶模型与简化动力学：在许多应用中，可以采用降阶模型或简化动力学模型来近似描述系统的行为，而不是使用全阶或复杂的非线性模型。例如，在自动驾驶车辆的轨迹跟踪中，可以使用自行车模型或线性化的动力学模型来预测车辆运动，而非复杂的非线性八自由度模型。这种简化虽然可能牺牲一定的模型精度，但能大幅降低预测和优化问题的维度和复杂性，从而减少计算量。
  • 模型参数量化与稀疏化：借鉴深度学习领域的模型压缩技术，对MPC模型中的参数进行量化（如从浮点数转换为定点数）或稀疏化处理。参数量化可以减少模型存储空间和计算时的内存带宽需求，而稀疏化则可以利用稀疏矩阵运算的优势，加速计算。
  • 预测时域与控制时域裁剪：通过缩短预测时域（prediction horizon）和控制时域（control horizon）来降低优化问题的规模。较短的时域意味着需要优化的变量数量减少，从而加速求解过程。然而，这需要在控制性能（如鲁棒性、前瞻性）和计算资源之间进行权衡。
  • 显式MPC的优化存储：显式MPC通过离线计算将控制律存储为分段仿射函数，在线查询。虽然原始显式MPC的存储需求可能很高，但通过优化临界区域的表示方式（如采用决策树、kd-tree等数据结构）或仅存储部分关键区域，可以有效减少内存占用，使其更适合边缘部署。Nielsen 提出的减少显式MPC所需内存的算法，旨在使mp-QP和显式MPC在嵌入式系统等内存受限的实际应用中更具可用性，通过利用QP问题在参数化解中的结构来减少内存占用，是模型裁剪的一个典型例子。

3.2.2 并行计算优化方案

端边设备，特别是高性能边缘计算平台，通常配备多核CPU、GPU、FPGA或DSP等异构计算单元。利用这些硬件的并行计算能力来加速MPC的求解过程是轻量化设计的另一重要方向。

  • 多核CPU并行：将MPC优化问题分解为可以独立或半独立求解的子任务，并在多核CPU上并行执行。例如，一些优化算法（如ADMM）天生适合并行化。对于分布式MPC，各个子系统控制器可以并行计算其局部优化问题，再通过通信协调。Necoara和Clipici 提出了一种针对分布式MPC的并行坐标下降算法，用于解决具有可分离约束的凸优化问题，这展示了并行算法在提高MPC效率方面的潜力 101。
  • GPU加速：图形处理器（GPU）凭借其海量的并行计算单元，在矩阵运算、数值优化等任务上具有显著优势。将MPC优化问题中的密集型计算（如矩阵乘法、线性方程组求解）卸载到GPU上，可以大幅缩短求解时间。
  • FPGA/ASIC定制硬件：对于对实时性要求极高的应用（如高频振动控制、毫秒级机器人动作），可以考虑设计定制的FPGA（现场可编程门阵列）或ASIC（专用集成电路）来硬件加速MPC的求解器。FPGA允许将优化算法直接映射到硬件逻辑上，实现超低延迟和高吞吐量的并行计算。Ferranti等 提出的基于算子拆分方法的无限时域CLQR算法，由于其分解为无约束最小二乘问题和梯度计算的结构，也非常适合在FPGA上进行高效实现。
  • 模型预测控制的并行化：Long等 提出了一种并行移动阻塞MPC算法，旨在利用多核处理器、FPGA或GPU等并行计算架构。通过同时解决多个较小的优化问题，可以缩短计算延迟，从而允许更快的采样率，并在闭环成本方面优于标准MPC公式。通过适当选择所谓的阻塞矩阵，可以保证可行性和稳定性 102。这种方法通过将大型问题分解为一系列可并行处理的小问题，有效提升了计算效率。

3.2.3 端边架构与高动态场景的适配

端边MPC的轻量化设计最终目标是满足高动态场景（如高速行驶的车辆、快速移动的机器人）的毫秒级求解需求。

  • 硬件-软件协同设计：实现毫秒级求解不仅仅是优化算法，更需要软硬件协同设计。例如，选择合适的嵌入式处理器（如ARM Cortex-R系列、NVIDIA Jetson系列），并针对其架构特点对MPC求解器进行底层优化。利用硬件中断和DMA（直接内存访问）等机制，减少CPU的开销，确保控制指令能及时发出。
  • 分布式计算与联邦学习：在某些场景下，端边设备之间可以形成一个计算网络。分布式MPC本身就是一种利用多节点计算能力的体现。此外，联邦学习（Federated Learning）等技术，例如参考文献103中提出的增强隐私和溯源的IoHT框架，或参考文献104中提到的智能农场大数据智能决策模型，都强调了联邦学习在分布式数据处理和模型训练中的潜力。虽然这些文献未直接将联邦学习与MPC结合，但其理念为在保护数据隐私的前提下提升边缘设备的智能化水平和决策能力提供了借鉴。在微电网管理中，AI驱动的分布式能源管理系统可以利用MPC进行优化，参考文献105详细探讨了MPC在微电网中的应用，强调其在优化性能、效率和弹性方面的作用。参考文献106则综述了AI在智能本地微电网和能源社区中的应用，包括混合模型预测控制和联邦及边缘AI的进步，这表明将MPC与联邦学习结合以适应动态变化的负荷需求和可再生能源输出，具有潜在的研究和应用价值。
  • 弹性计算与资源管理：考虑到边缘设备资源有限且可能波动，MPC系统需要具备一定的弹性。这包括根据当前计算负载和可用资源动态调整MPC参数（如预测时域），或者在资源紧张时切换到更简单的控制策略（如回退到PID控制），以确保基本功能得以维持。

综上所述，端边架构适配的MPC轻量化设计是一个多维度、系统性的工程。通过模型裁剪、充分利用并行计算硬件以及软硬件协同优化，可以有效地将MPC的强大功能扩展到资源受限的边缘设备，满足自动驾驶和机器人等高动态应用对毫秒级实时控制的严苛要求，开启MPC应用的新篇章。

3.3 数据驱动融合的MPC求解加速

随着数据科学和机器学习技术的飞速发展，将数据驱动方法与模型预测控制（MPC）相结合，成为提升MPC求解效率、降低计算开销、应对复杂动态和不确定性的重要途径。这种融合旨在利用机器学习（ML）强大的模式识别和预测能力，优化MPC的决策过程，特别是在约束预判、热启动优化等方面，从而加速求解过程并提升复杂场景下的控制性能。

3.3.1 机器学习模型辅助MPC约束预判

MPC在每个控制周期需要在线求解一个优化问题，其中约束条件（如安全边界、设备限制、交通规则等）的准确、实时处理是其复杂性来源之一。机器学习模型可以辅助MPC对未来可能违反的约束进行预判，从而更有效地引导优化器，减少不必要的迭代。

  • 神经网络预测器：神经网络因其强大的非线性映射能力，可以用来学习系统的复杂动态和外部扰动对约束的影响。例如，在自动驾驶中，神经网络可以根据当前环境感知数据和历史驾驶行为，预测未来几秒内交通参与者的轨迹，并据此提前预判潜在的碰撞风险区域。这些预测结果可以转化为MPC的软约束或硬约束，指导路径规划和行为决策。文献107指出，机器学习方法，尤其是神经网络，能够准确地建模复杂的动态效应，这为MPC提供了更精确的预测模型，虽然计算复杂度高，但其代表能力显著。将此类预测模型与MPC结合，可以实现更精准的约束管理。
  • 安全临界区预测：在机器人和自动驾驶等安全攸关领域，机器学习可以学习历史数据中安全边界的模式。例如，通过分析大量驾驶数据，可以训练一个分类器来预测哪些驾驶情境可能导致车辆接近车道边界或与其他车辆发生碰撞。MPC在优化时可以优先考虑这些由ML模型识别出的高风险区域，并通过调整控制权重或提前规划规避动作来避免潜在危险。文献34强调了安全学习在机器人领域的兴起，指出学习型控制方法能够安全地提升性能，并通过预测性安全滤波器确保系统在学习型策略可能不安全的情况下依然满足安全约束。
  • 优化变量初始化与可行性区域估计：机器学习模型可以根据历史最优解或专家经验，为MPC的优化问题提供一个高质量的初始猜测。一个良好的初始点可以显著减少优化器收敛所需的时间。此外，ML模型还可以辅助估计优化问题的可行区域，排除明显不可行的解空间，从而缩小搜索范围，加速求解。

3.3.2 热启动优化（Warm Start Optimization）

MPC的“滚动优化”特性意味着在连续的控制周期中，相邻优化问题的解往往非常接近。热启动（Warm Start）利用上一个控制周期的最优解或其邻近信息作为当前周期的初始猜测，能够显著加快优化器的收敛速度。数据驱动方法可以在此基础上提供更智能的热启动策略。

  • 机器学习预测最优解：可以训练机器学习模型（如回归树、神经网络）来预测给定当前系统状态和环境输入下的最优控制输入序列或状态轨迹。这个预测结果可以作为当前MPC优化问题的热启动点，比简单地使用上一个周期的解更具前瞻性和准确性，尤其是在系统发生较大变化或面临新扰动时。文献108提到，机器学习算法可以学习MPC的简化控制律，尤其是在处理多输入多输出（MIMO）问题时，通过深度时延神经网络和回归树来学习控制输入对参数的依赖性，并在保持性能的同时显著降低了复杂性和实现成本。这种学习到的控制律本身就可以作为热启动的依据。
  • 条件变分自编码器（CVAE）暖启动：文献109提出了一种创新的方法，将带有条件变分自编码器（CVAE）的学习型暖启动策略应用于自动驾驶的双层优化问题。CVAE能够学习并生成多样化的、符合任务要求的行为层决策和下游轨迹。通过预先学习的CVAE模型，MPC可以获得高质量的初始轨迹，从而在实时运行中加速优化求解。这种方法在保证驾驶效率的同时，显著降低了碰撞率，证明了数据驱动暖启动策略的有效性。
  • 迭代学习与热启动相结合：在重复性任务或具有周期性行为的系统中，可以将迭代学习控制（Iterative Learning Control, ILC）的思想与MPC的热启动相结合。通过学习前几次迭代的最优控制序列，ML模型可以为当前迭代提供更好的初始猜测，从而在每次任务执行中逐步提升MPC的效率和性能。

3.3.3 降低重复求解的计算开销，提升复杂场景下的求解效率

数据驱动与MPC的融合不仅限于约束预判和热启动，更深层次的目标是降低MPC在面对高动态、强不确定性和大规模系统时的重复求解计算开销，从而提升其在复杂场景下的实时性和求解效率。

  • 代理模型（Surrogate Model）与模型降阶：对于复杂的非线性系统，建立精确的第一性原理模型成本高昂，且用于MPC的在线优化计算量大。机器学习可以构建轻量级的代理模型来替代部分或全部第一性原理模型，用于MPC的预测。例如，利用神经网络学习系统的输入-输出映射，构建一个快速响应的预测器。这种代理模型可以显著降低预测步骤的计算负担，但需要确保其精度足够满足控制要求。文献110提出了一种基于Koopman算子理论的数据驱动方法，利用神经网络框架来线性化混合车辆编队模型，并在此基础上设计了MPC算法，实现了与非线性模型相当的控制性能，但计算成本更低，收敛速度更快。文献72展示了如何将神经网络模型与第一性原理模型相结合，应用于实时优化（RTO）和MPC，有效处理了CSTR和精馏塔等复杂化学过程中的非线性动态，并在经济效益上表现出优势。
  • 数据驱动的MPC策略学习：在某些情况下，可以直接训练机器学习模型来近似MPC的控制律，形成一个“代理控制器”。例如，通过模仿学习（Imitation Learning）或强化学习（Reinforcement Learning, RL）训练一个神经网络，使其在给定状态下输出与MPC相似的控制动作。一旦训练完成，这个神经网络的推理速度远快于在线MPC优化，从而实现超高速的控制响应。文献111比较了深度强化学习（DRL）和MPC在自适应巡航控制（ACC）中的表现，发现在没有建模误差且测试输入在训练数据范围内时，DRL解决方案与MPC的性能相当。当存在建模误差时，DRL甚至表现出更好的性能。文献112提出了一种将深度神经网络（DNN）与MPC结合的强化学习控制器，用于风力涡轮机的扭矩和变桨控制，该数据驱动策略适应系统动态变化，提高了控制性能和鲁棒性。
  • 混合MPC与分层控制：数据驱动方法也可以与MPC在分层控制架构中协同工作。上层决策或规划层可以使用更复杂的ML模型进行长期预测和策略生成，然后将这些信息传递给底层的MPC控制器，MPC则负责短时域内的精确轨迹跟踪和约束满足。这种结合利用了ML的全局感知和高层决策能力，以及MPC的局部优化和实时执行能力。文献113提到了一种用于并网风光微电网的协调优化运行MPC策略，该策略包含了混合储能管理系统，旨在延长储能设备的寿命并管理电力和氢气的生产。文献114指出，经典的MPC在建筑能源管理中有效，但存在建模劳动密集和在线优化复杂的问题，而数据驱动的MPC和基于强化学习的方法则提供了解决方案。该文献强调了这两种方法结合的潜力，以应对建筑能源管理中的挑战。文献115则综述了建筑供暖和制冷系统中数据驱动和混合模型的能源建模与控制，讨论了MPC和RL控制技术的前沿发展，并强调了结合数据驱动和物理模型的必要性，以应对复杂的动态系统和不确定性。
  • 模型学习与验证：文献107提出了一种“实时神经MPC”框架，能够将大型、复杂的神经网络架构作为动力学模型集成到MPC管道中。该框架在四旋翼飞行器上进行仿真和实测，证明了其在嵌入式平台上运行大型学习模型的能力，并将位置跟踪误差降低了高达82%，这表明机器学习模型能够显著提升MPC的预测精度和性能。

通过上述数据驱动与MPC的融合技术，研究人员正致力于突破传统MPC在实时性、计算开销和复杂场景适应性方面的瓶颈，使其在自动驾驶、机器人和工业过程控制等高要求领域发挥更大的作用。这种融合不仅提高了控制系统的智能化水平，也为未来的自主系统发展奠定了基础。

4. MPC鲁棒性增强与安全约束保障机制

4.1 不确定场景下的鲁棒MPC设计

在现实世界的复杂动态系统中，诸如模型失配、外界扰动、参数漂移以及传感器噪声等不确定性无处不在。这些不确定性可能导致模型预测控制（MPC）的预测精度下降，甚至引发系统性能恶化或违反安全约束。因此，鲁棒MPC（Robust Model Predictive Control, RMPC）的设计旨在增强控制系统在不确定条件下的抗干扰能力，确保系统性能和约束满足度。鲁棒约束构建和Tube MPC是目前研究最广泛和有效的两种方法。

4.1.1 鲁棒约束构建

鲁棒约束构建的核心思想是在优化问题中显式地考虑不确定性的影响，从而收紧名义约束，确保在所有可能的不确定性实现下，实际系统状态和控制输入都不会违反原始约束。

  • 集中式鲁棒MPC：传统的鲁棒MPC方法通常采用最坏情况优化（Worst-Case Optimization）的思想，即在所有可能的不确定性集合中，寻找一个控制输入，使得即使在最恶劣的情况下，系统约束也能被满足。Kothare等 116 提出的基于线性矩阵不等式（LMI）的鲁棒MPC方法，通过在优化问题中引入LMI，能够处理具有有界范数扰动的线性系统，并在保证鲁棒稳定性的前提下，实现约束的满足。这种方法虽然在理论上提供了强有力的鲁棒性保证，但通常会导致较为保守的控制性能，且计算复杂度较高。
  • 概率鲁棒MPC（Chance-Constrained MPC）与场景优化：为了在鲁棒性和性能之间取得更好的平衡，概率鲁棒MPC允许约束以一定概率被违反，而不是在所有情况下都严格满足。这种方法在处理随机不确定性时尤其有效。
    • 场景优化（Scenario Optimization）：Calafiore和Fagiano 117118 提出了一种基于场景优化的概率方法来设计鲁棒MPC律，用于处理受参数不确定性和附加扰动影响的离散时间线性系统。该技术在每个步骤迭代求解一个有限时域最优控制问题（FHOCP），该问题考虑了足够数量的随机提取的不确定性和扰动场景，并结合预测时域内的特定指令选择规则。场景FHOCP始终是凸的，即使不确定参数和扰动属于非凸集合，并且无论模型不确定性如何影响系统矩阵。此外，该方法的计算复杂度不依赖于不确定性/扰动维度，而是与控制时域呈二次关系。该研究的主要成果表明，所设计的控制律以预先设定的概率$p$保证在每个步骤满足约束，同时系统的状态以至少$p$的概率渐近或在有限时间内达到目标集。这种方法在传统确定性或随机技术因过度保守或非凸问题导致数值难以处理时，提供了一种有效的替代方案。Oldewurtel等 119 进一步研究了基于仿射扰动反馈的易于处理的概率约束随机MPC近似方法，用于处理输入具有多面体约束和状态具有概率约束的线性离散时间不确定系统，结果表明这种闭环预测公式可以进一步提高性能，同时满足预定义的概率约束。
  • 自适应鲁棒MPC：针对电机参数漂移等不确定性，Xu等 120121 提出了一种基于非线性扰动补偿的超局部模型预测电流控制（MFPCC）方法。该方法不涉及任何电机参数，能够更准确、稳定地估计系统总扰动并进行前馈补偿，实时更新控制信息，仅需调整两个控制参数。仿真结果表明，该控制方法具有高抗干扰性、高鲁棒性、小输出纹波和改进的动态特性。此外，他们还提出了基于参数扰动补偿的模型预测控制，通过监测电机参数漂移引起的系统扰动并进行实时补偿，有效避免了参数变化引起的电流静差和振荡问题，具有良好的动态性能和抗干扰能力 121。这些研究表明，通过对不确定性源进行实时估计和补偿，可以设计出自适应的鲁棒MPC控制器。

4.1.2 Tube MPC（管式MPC）

Tube MPC是一种有效处理有界扰动或不确定性的鲁棒MPC方法，其核心思想是为名义系统轨迹构建一个“管”（tube），并保证在所有可能的不确定性实现下，实际系统轨迹始终包含在这个管内。

  • 基本原理：Tube MPC将鲁棒控制问题分解为两个部分：一个名义MPC控制器负责计算中心轨迹，并收紧约束以容纳管的半径；一个辅助控制器（通常是线性反馈控制器）负责将实际系统轨迹限制在以名义轨迹为中心的管内。这种分解使得主MPC优化问题保持较低的维度，从而提高了计算效率。Limón等 122 提出了针对具有加性扰动的受约束线性系统的鲁棒管式MPC跟踪方法，并进一步扩展了Tube MPC框架。
  • 鲁棒性与稳定性保证：Tube MPC通过将扰动的影响建模为一个有界集合（即“管”），可以提供对系统状态和输入约束的鲁棒满足保证，以及闭环系统的渐近稳定性。Carson 123 提出了一种R-MPC（Robust and re-solvable MPC）算法，通过一个单独的反馈组件（离线确定）生成一个不变管，确保实际系统轨迹在名义前馈轨迹附近。该管还提供了理论上保证R-MPC算法持续可行性和可重解性的手段，这两者都是保证渐近稳定性所必需的。
  • 应用领域：Tube MPC在多种工业和工程应用中展现出优势。
    • 高精度滚筒生产系统：Chen等 124 设计了一种鲁棒线性参数变化模型预测控制（LPV-MPC）方案，用于增强高精度滚筒（R2R）生产系统的张力跟踪性能。该方案引入了一个管式MPC公式，结合调度参数，充分更新模型并纠正时变动态。约束条件被纳入MPC以保持控制器可靠性并避免机器故障。仿真结果表明，该控制器在快速瞬态响应和无偏移张力跟踪方面优于基准测试，并且对参数不确定性引起的变化具有免疫力。
    • 航空航天和机械车辆：Carson 123 的研究特别指出，Tube MPC适用于航空航天和机械车辆等需要在线实现且具有严格物理约束的工程应用。其SR-MPC（Safety-mode augmented R-MPC）算法通过将反应性安全模式与R-MPC算法相结合，在保证系统渐近收敛的同时，提供了对意外状态约束变化的鲁棒性。
    • 复杂系统控制：除了上述应用，Tube MPC还被广泛应用于过程控制、机器人运动规划等领域，特别是当系统面临持续性、有界扰动时，Tube MPC能够在保证性能的同时有效维护系统安全。Kouvaritakis和Cannon 125 的专著对经典、鲁棒和随机模型预测控制进行了全面概述，其中也详细探讨了Tube MPC等鲁棒设计方法。
    • COVID-19疫情预测控制：Köhler等 126 将鲁棒和最优预测控制应用于COVID-19疫情的预测控制，在不确定性下保持对病毒传播的控制，这也反映了鲁棒MPC在应对复杂社会系统不确定性方面的潜力。

总体而言，鲁棒约束构建和Tube MPC是处理不确定性的关键技术，它们通过不同的策略增强了MPC在复杂环境下的可靠性和安全性。随着计算能力的提升和算法的优化，这些鲁棒MPC方法有望在自动驾驶、机器人和工业过程控制等领域发挥更加关键的作用，从而实现更安全、更可靠、更高效的自主控制系统。

4.2 硬安全约束嵌入与冲突消解策略

在自动驾驶、机器人和工业过程控制等安全攸关领域，确保系统在任何操作条件下都能满足严格的安全约束是至关重要的。模型预测控制（MPC）通过将其作为优化问题的显式约束来处理这些安全要求，这比传统控制方法更具优势。然而，当多个硬约束同时存在并可能发生冲突时，需要设计有效的策略来消解这些冲突，并确保最关键的安全约束始终得到满足。

4.2.1 硬安全约束嵌入MPC优化目标的方法

将硬安全约束嵌入MPC优化目标通常意味着将这些约束表达为数学不等式或等式，并将其作为优化问题的必须满足的条件。一旦这些约束被违反，系统可能面临灾难性的后果（例如碰撞、设备损坏、人员伤害）。

  • 自动驾驶中的交通规则与碰撞避免：
    • 交通规则：自动驾驶车辆必须遵守交通法规，如限速、车道保持、交通信号灯规则等。这些规则可以直接转化为MPC的硬约束。例如，车辆速度不能超过当前路段的限速；在变道时，必须确保有足够的安全距离。Tsolakis等 127 提出了一种用于自主水面船舶（ASV）的符合交通规则的轨迹优化方法，该方法基于模型预测轮廓控制（MPCC），并将国际海上避碰规则（COLREGs）相关规定融入运动规划。通过将这些规则转化为MPC优化问题中的约束条件，该方法能够生成遵循规则的机动行为，适用于混合交通环境。
    • 碰撞避免：这是自动驾驶中最核心的安全约束之一。MPC通过在预测时域内预测自车和周围障碍物（包括其他车辆、行人、静态物体）的未来轨迹，并确保在整个预测时域内两者之间保持最小安全距离。Ji等 128 提出了一种基于多约束MPC（MMPC）的路径规划和跟踪框架，通过构建一个三维虚拟危险势场来生成避障轨迹，并利用MMPC计算前轮转向角以避免与移动障碍物碰撞，仿真结果表明该方法在动态避障方面是有效的。Abdelaal等 129 也提出了针对欠驱动船舶的非线性MPC，用于轨迹跟踪和碰撞避免。Kim和Kumar 130 提出了一种基于MPC的方法，用于开发可证明无碰撞的自动地面交通系统，并提出了自动交叉路口管理框架。该方法通过将邻近车辆状态、速度限制、最大加减速等约束纳入MPC优化框架，并结合车辆间的协调规则，确保了交通系统的系统级安全和活跃性。此外，Brito等 131 提出了一种用于非结构化动态环境中避碰的非线性模型预测轮廓控制（MPCC）方法。该方法通过在线计算自由空间中的凸区域来结合静态地图，并将移动障碍物建模为椭圆以近似碰撞区域，实现了机器人（包括自动驾驶汽车）在有人类环境中导航时的有效避障。
    • 代理安全指标（SSM）：Dai等 132 将代理安全指标（SSM）显式地整合到MPC的纵向控制目标中，以增强队列安全性。SSM被广泛用于评估车辆控制策略的安全后果和识别潜在的近碰撞事件。该研究构建了一个状态空间MPC算法，将三种典型的SSM（例如时间裕度TTC）纳入控制目标，并通过数值示例和微观交通仿真验证了其在降低追尾碰撞风险方面的有效性。
  • 机器人中的避障与力位限制：
    • 运动学与动力学约束：机器人的关节角度、关节速度、关节力矩、末端执行器速度等都存在物理限制，这些都必须作为硬约束嵌入MPC。例如，机械臂不能超出其工作空间，关节速度不能超过电机最大转速。
    • 碰撞避免：与自动驾驶类似，机器人也需要避免与环境中的障碍物（包括静态和动态障碍物）以及自身构件发生碰撞。MPC通过在优化中包含碰撞检测模型和安全距离约束来实现避障。Hong等 133 提出了一种结合深度强化学习（DRL）和MPC的混合路径规划框架，以实现无碰撞机器人路径规划。DRL生成短期参考轨迹，MPC通过约束感知优化来细化轨迹，确保及时避障。该方法在动态障碍物环境中显著提高了避障成功率、轨迹平滑度和路径精度。
    • 力交互约束：在协作机器人或需要与环境进行物理交互的机器人应用中，末端执行器与环境之间的接触力需要被限制在安全范围内，以避免对机器人或环境造成损坏。Piccinelli和Muradore 提出了一种用于位置控制机械手的线性MPC方法，通过将交互力作为约束集成到MPC中，成功在UR5e协作机器人上验证了其在安全关键场景中控制交互力的能力。
  • 工业过程控制中的工艺安全阈值：
    • 操作限值：工业过程中的温度、压力、液位、浓度等变量都存在严格的安全操作上下限。MPC必须始终确保这些工艺变量保持在允许的范围内，以防止设备损坏、产品变质甚至安全事故。例如，反应釜的温度不能过高以避免爆炸，精馏塔的液位不能过低以防止泵空转。
    • 设备保护：执行器（如阀门、泵、加热器）的输出能力也是硬约束，MPC需要尊重这些物理限制。
    • 质量规格：某些产品质量指标（如纯度、粘度）可能被视为硬约束，必须在允许的公差范围内。

4.2.2 多约束冲突时的优先级动态调度机制

在复杂的系统中，尤其是在紧急情况或极端操作条件下，MPC优化问题中定义的多个硬约束可能会发生冲突，即无法同时满足所有约束。例如，在自动驾驶中，既要避让突然出现的障碍物，又要保持在车道内，同时还要遵守限速，这些约束可能在某些危急时刻无法兼顾。此时，需要一个智能的优先级调度机制来决定哪些约束必须被满足（硬约束），哪些可以适度放松（软约束），以及如何选择性地违反次要约束以满足更关键的约束。

  • 基于优先级的约束松弛（Prioritized Constraint Relaxation）：
    • 分层优先级：最常见的方法是为每个约束分配一个优先级。在优化问题中，将优先级最高的约束视为硬约束，必须满足。对于较低优先级的约束，可以引入松弛变量（slack variables），并将其违反惩罚项加入到目标函数中。当约束冲突发生时，优化器会尽可能满足高优先级约束，同时允许低优先级约束在最小惩罚的前提下被违反。Vada等 134 135 提出了针对具有优先级的线性MPC中不可行性处理的算法。该算法能够通过在线求解一个额外的线性规划（LP）问题，将一个不可行的优先级MPC优化问题最优地松弛为一个可行的问题，确保高优先级约束的违反不会因减少低优先级约束的违反而增加。这在实践中非常重要，例如在电池管理系统中，通过MPC可以平衡电池的健康、安全和性能，处理如过充、过放、热失控等硬约束。
    • 词典序优化（Lexicographic Optimization）：Lexicographic Optimization 是一种处理多目标优化问题的方法，其中目标函数按照严格的优先级顺序进行优化。当多个约束具有不同的优先级时，可以将它们转化为一系列按优先级顺序排列的优化问题。首先优化最高优先级的目标，得到一个最优解集；然后在这个解集中，优化次高优先级的目标，依此类推。这种方法保证了高优先级目标不会为了改善低优先级目标而牺牲其性能。Wang等 136 提出了一种基于词典序优化（LO-MPC）的MPC框架，用于自动驾驶中的伦理决策。该方法允许将障碍物和约束按照优先级进行排序。例如，在不可避免的碰撞场景中，可以优先保护车内乘员，其次是行人，最后是财产。仿真结果表明，LO-MPC能够通过避免具有预设优先级的障碍物来处理伦理决策，相比传统决策算法具有优势。
  • 软约束与惩罚函数：除了硬约束，MPC还可以使用软约束。软约束允许在一定程度上被违反，但会在目标函数中引入惩罚项。惩罚的权重越大，控制器就越倾向于满足该约束。通过动态调整这些惩罚权重，可以实现约束的动态调度。例如，在正常情况下，保持舒适性是一个重要目标，其惩罚权重较高；但在紧急避障时，为了避免碰撞，舒适性约束的惩罚权重可以降低，甚至暂时忽略，以允许更激进的机动。Gatzke和Doyle 137 讨论了在MPC中使用软输出约束和优先级控制目标，可以使控制器在面对冲突时，根据预设的优先级进行权衡。
  • 状态依赖约束松弛：根据系统当前的状态和预测的未来状态，动态调整约束的优先级和松弛策略。例如，当车辆距离障碍物较远时，所有约束（包括舒适性、能耗）都可能是硬约束；但当距离障碍物过近，碰撞风险极高时，避障约束会升级为最高优先级，其他约束（如舒适性、燃油经济性）可以被大幅度松弛。
  • 混合整数规划（MIP）：对于涉及离散决策（如车辆变道、路径选择）和连续变量（如车速、转向角）的复杂场景，可以通过引入二元变量将优先级和约束冲突消解问题建模为混合整数规划（MIP）问题。通过MIP，MPC可以同时优化离散决策和连续控制输入，从而在多约束冲突时做出最优的取舍。Cataldo和Scattolini 138 在废弃物处理厂的动态托盘路径优化控制中，提出了基于混合MPC的方法，通过将工厂数学表示为混合线性动态（MLD）模型，并将要最小化的性能指标设置为线性权重，来递归求解产生的混合线性整数规划（MILP）问题，这可以用于处理优先级冲突的调度问题。Nakamura等 139 提出了半导体制造厂中高架吊车（OHT）系统的调度方法，利用MPC策略解决动态调度问题，并引入切换型多目标成本函数，有效地将新的运输请求加入到调度中。
  • 安全屏障函数（Control Barrier Functions, CBFs）与MPC结合：CBF作为一种新兴的安全保证工具，可以与MPC结合使用。CBF能够为系统定义一个“安全集”，并确保系统状态不会离开这个安全集。当MPC的优化结果可能导致违反CBF定义的安全性时，CBF可以作为一个附加的约束，强制MPC调整其控制输出以保持系统安全。Zhang等 140 提出了一种“礼貌MPC”（Courteous MPC）方法，用于自动驾驶车辆，该方法结合了CBF启发的风险评估框架，以确保AVs在共享道路上与人类驾驶车辆交互时的安全和礼貌行为。它将风险评估框架整合到MPC中，以生成礼貌行为，同时降低对其他车辆造成的总风险，并尊重硬安全约束。Sabouni等 141 开发了一个分层控制器，其中协调器确定一个安全序列（SS），然后低级分布式运动控制器为每个联网自动驾驶车辆（CAV）最小化行驶时间和能量，同时满足基于CBF的硬安全约束，从而在混合交通中提供安全合并的保证。

通过上述硬安全约束嵌入和优先级调度机制，MPC能够有效地处理复杂、动态和安全攸关的应用场景。这不仅提高了系统的可靠性和安全性，也使得MPC成为实现未来自动驾驶、机器人和高度自动化工业生产不可或缺的关键技术。

4.3 故障场景下的容错MPC控制机制

在自动驾驶、机器人和工业过程控制等高可靠性应用中，传感器故障、执行器卡顿或失效等异常场景是不可避免的。传统的控制系统在面临这些故障时可能导致性能急剧下降甚至系统崩溃。容错控制（Fault-Tolerant Control, FTC）旨在使系统在部分组件失效的情况下仍能保持其关键功能，或者至少能够安全降级运行。模型预测控制（MPC）由于其内在的优化和约束处理能力，为实现先进的容错控制提供了强大的框架。容错MPC（FTMPC）通常涉及故障检测与隔离（FDI）、控制律重构以及安全降级策略。

4.3.1 故障类型与FTMPC应对概述

MPC能够应对多种故障类型，包括：

  • 传感器故障（Sensor Faults）：如传感器漂移（bias）、量程误差（scaling error）、卡顿（stuck at a value）、断线（out-of-range）或完全失效（failure）等。这些故障会导致MPC接收到错误的系统状态信息，从而做出错误的控制决策。
  • 执行器故障（Actuator Faults）：如执行器饱和（saturation）、效率损失（loss of effectiveness）、卡顿（stuck）、偏置（bias）或完全失效等。这些故障会限制MPC控制输出的实际作用，导致期望控制效果无法实现。
  • 过程故障（Process Faults）：如模型参数漂移、过程泄漏、反应器堵塞等，这些会改变系统的动态特性，使得MPC的预测模型失配。

FTMPC通过以下机制应对这些故障：首先，故障检测与隔离（FDI）模块实时监测系统行为，一旦发现异常，立即识别故障类型和位置。其次，控制律重构（Control Reconfiguration）模块根据FDI结果调整MPC的预测模型、成本函数或约束，以补偿故障影响。最后，在无法完全补偿故障或故障过于严重时，启动安全降级（Safe Degradation）策略，使系统进入一个更安全、但可能性能较低的操作模式。

4.3.2 传感器故障下的FTMPC

传感器故障是工业系统中最常见的故障之一，其直接影响是导致MPC的状态估计不准确。

  • 冗余配置与软传感器：部署多个传感器形成冗余配置是提高可靠性的直接方法。当一个传感器失效时，可以通过其他传感器提供的信息进行交叉验证或替换。此外，软传感器（基于其他可测变量构建的估计器）可以用来估计关键变量，作为物理传感器的补充或替代。
  • 基于观测器的故障估计：卡尔曼滤波器（Kalman Filter, KF）及其变种（如扩展卡尔曼滤波器EKF、无迹卡尔曼滤波器UKF）常用于状态估计和故障估计。当传感器发生故障时，观测器可以利用系统的动力学模型和可靠的传感器数据来估计故障传感器的真实值，或直接估计故障本身。
    • Prakash等 提出了一种将基于广义似然比的故障检测与识别（FDI）方法与MPC的状态空间表述相结合的主动在线容错MPC方案。该方案使用卡尔曼滤波器作为基础，实现了MPC与FDI的紧密集成，能够在传感器或执行器存在偏置或漂移等软故障时，通过由FDI组件识别的合格位置进行偏差校正，消除控制变量真实值与设定点之间的偏差，并确保状态变量、操纵输入和测量变量的真实值维持在规定范围内。
    • Veerasamy等 将遗传算法调优的自适应遗忘记忆卡尔曼滤波器与MPC控制器集成，用于处理传感器故障，特别是当噪声协方差不准确时，进一步提升了故障估计的鲁棒性。
  • MPC与故障估计算法的集成：在自适应巡航控制（ACC）系统中，针对毫米波雷达传感器故障，Zhang等 提出了一种主动容错控制方案。该方案将传感器故障视为离散事件，构建了ACC上层控制系统的混合逻辑动态（MLD）模型，其中包含无故障动态和故障动态。在此MPC框架下，即使在雷达传感器失效的情况下，车辆也能安全平稳行驶，证明了该方法对于提高车辆自身智能性和确保安全驾驶的重要性。
  • PMSM电机传感器故障容错：Benkaihoul Said等 提出了一种混合容错控制（FTC）架构，用于永磁同步电机（PMSM）在转速传感器故障（SSF）下的运行。该架构整合了MPC、三阶滑模控制（TOR-SMC）和模型参考自适应系统（MRAS）。MRAS能够实现高保真度转速估计，一旦残差式故障检测机制识别出故障，系统可无缝切换到基于观测器的控制。该系统将速度估计误差降低至1.8%，跟踪精度达97.6%，故障检测时间快41.3%。
  • 无人机传感器故障容错：Diget等 提出了一种多旋翼无人机（UAV）的先进容错控制方法，包括传感器测量异常检测、执行器故障估计和鲁棒MPC。利用回声状态网络（Echo State Network）检测传感器异常，自适应扩展卡尔曼滤波器估计系统状态和故障，然后用MPC进行控制。仿真结果表明，该FTC方案能够处理不同类型（偶发和非偶发）的执行器故障。

4.3.3 执行器故障下的FTMPC

执行器故障直接影响MPC的控制输出能力，可能导致系统无法达到期望的性能或维持稳定。

  • 控制分配与重构：当部分执行器失效或效率降低时，FTMPC需要重新分配剩余可用的执行器资源，以尽可能地维持控制目标。
    • Yu和Zhang 针对波音747-100/200飞机的非线性基准模型，提出了一种基于Laguerre函数MPC（LF-MPC）的容错控制方案。LF-MPC能够有效利用剩余功能执行器，通过减少优化参数来提高在线容错能力。该方法在襟翼在着陆过程中卡顿的场景下，成功使飞机安全着陆。
    • Azmi 提出了针对变速风力涡轮机系统中使用LMI的MPC控制器设计，并考虑了执行器故障（包括偏置、效率损失、卡顿和失效）下的新型FTC策略，通过MPC和故障估计方案来消除执行器故障和扰动的影响。
  • 模型更新与约束调整：执行器故障通常意味着模型中与该执行器相关的输入矩阵或约束条件需要更新。例如，如果一个阀门卡顿，其输出变为常数，则MPC模型中对应的控制输入应被移除，并将其作为已知扰动或固定输入处理。如果执行器效率损失，则相应输入约束会收紧。
  • 混合逻辑动态（MLD）建模：对于执行器故障导致的系统模式变化（如一个电机失效使多旋翼无人机从六旋翼变为五旋翼），可以采用MLD模型来描述不同故障模式下的系统动态。MPC可以在FDI模块识别出故障模式后，切换到对应的MLD模型进行优化，从而实现适应性重构。
    • Tang等 提出了一种针对旋翼完全失效的四旋翼无人机容错轨迹跟踪控制问题，通过牺牲偏航控制来解决欠驱动问题。该方案采用分层控制，上层使用MPC进行轨迹跟踪并考虑执行器饱和，内层使用基于增量非线性动态逆（INDI）的控制器稳定姿态并消除外部扰动。仿真结果验证了该方法在外部扰动、模型不确定性和完全旋翼失效情况下的有效性。
    • Escobar-Jiménez等 提出了一种基于多输入多输出（MIMO）MPC的实验性容错控制实现，旨在使双管逆流换热器在主执行器卡顿的情况下仍能继续运行。通过自适应观测器实现故障检测与隔离（FDI），并将MPC的控制信号与观测器估计的冷热水流量进行比较，验证了该FTC方法的有效性。
  • 电驱动系统容错：Chakraborty和Das 提出了一种针对感应电机驱动系统中电流传感器故障的容错控制（FTC）算法。该算法采用两段式数学故障检测与隔离器（MFDI），在高低速下分别通过三阶和单离散微分算子检测故障。在故障隔离后，通过电流合成器估计定子电流，从而实现对电流传感器故障的FTC。

4.3.4 安全降级控制方案

当故障严重到无法通过控制律重构完全补偿，或者系统资源不足以维持正常性能时，安全降级是确保系统安全的最后一道防线。

  • 性能目标调整：FTMPC可以通过修改成本函数中的权重或目标，来降低对性能的要求，优先保障安全性。例如，在自动驾驶中，如果传感器或执行器严重故障，系统可能无法维持高速巡航，此时FTMPC可以强制车辆减速，并寻找安全停车区域，优先保证乘员安全而非行驶效率。
  • 约束优先级调整：如前所述，在多约束冲突时，可以动态调整约束的优先级。在故障场景下，与安全相关的硬约束（如碰撞避免、保持稳定）将被赋予最高优先级，而其他如舒适性、经济性等约束则可以被放松或暂时忽略。
  • 预定义安全模式切换：系统可以预定义几种安全模式，每种模式对应一套简化的控制策略和更严格的安全约束。当发生严重故障时，FTMPC会触发切换到最合适的安全模式，例如，无人机在旋翼故障时自动切换到紧急降落模式。
  • 基于风险的决策：利用机器学习和风险评估模型，结合MPC在故障发生时动态评估风险，并选择风险最低的控制策略。这可能意味着牺牲短期性能以换取长期安全。

综上所述，容错MPC通过紧密结合故障检测与隔离、智能的控制律重构以及多层次的安全降级策略，显著提升了控制系统在不确定和故障场景下的可靠性和安全性。这是MPC走向更广泛、更关键应用领域的必然趋势，也是实现未来高度自主化系统的关键技术之一。

5. MPC产业化落地核心挑战与应对路径

模型预测控制（MPC）在理论上展现出强大的性能和多功能性，尤其是在自动驾驶、机器人和工业过程控制等复杂动态系统领域。然而，要将MPC技术从实验室环境成功推广到大规模的产业化应用，仍面临诸多核心挑战。这些挑战不仅涵盖技术层面，还包括经济、法规和社会接受度等多个维度。本节将深入分析MPC在不同领域的产业化落地瓶颈，并探讨相应的应对路径。

5.1 自动驾驶领域MPC落地挑战

自动驾驶是MPC最具前景的应用场景之一，但其产业化落地也面临着一系列严峻的挑战，主要体现在多场景适配、控制逻辑可解释性、车规级硬件适配以及法规与伦理等多个方面。

5.1.1 多场景适配的复杂性

自动驾驶车辆需要在各种复杂且动态变化的交通场景下安全、高效地运行，这对MPC的泛化能力和实时性能提出了极高的要求。

  • 环境不确定性：MPC的性能高度依赖于其预测模型的准确性。然而，自动驾驶面临的环境充满了不确定性，包括其他道路参与者的不可预测行为、突发事件（如行人突然闯入、前方事故）、恶劣天气（雨、雪、雾）以及道路施工等。这些不确定性导致预测模型难以精确捕捉所有情况，从而可能引发MPC决策的次优甚至危险。虽然鲁棒MPC和随机MPC（如27中在自动驾驶避碰任务中成功实现的随机MPC）能部分应对不确定性，但要覆盖所有极端和“长尾”场景，仍需进一步研究。
  • 多样化的交通规则与驾驶习惯：不同国家、地区乃至同一区域内的不同道路类型（高速公路、城市道路、乡村小径）都有其特定的交通规则和驾驶习惯。此外，与人类驾驶员混行时，自动驾驶车辆需要理解并适应人类驾驶员的多样化风格（激进、保守、犹豫等）。MPC需要具备足够的灵活性和适应性，以动态调整其控制策略，这使得MPC的设计和验证变得异常复杂。
  • 高动态复杂工况：自动驾驶车辆可能需要在高速行驶中进行紧急制动、急打方向避障，或在低速城市环境中应对频繁的启动停车、多车道汇流等复杂工况。这些场景要求MPC在极短的时间内（通常为毫秒级）做出精确而安全的决策，并输出控制指令，这对于计算资源和算法效率是巨大的考验。

应对方向：

  • 场景化定制与模块化设计：针对不同类型的驾驶场景（如高速巡航、城市跟车、泊车等），开发专门优化的MPC模块。通过分层或混合控制架构，在高层进行场景识别和模式切换，底层MPC负责特定场景下的精细控制。例如，可以针对高速公路场景优化MPC参数以追求平顺性和燃油经济性，而城市道路则更侧重避障和反应速度。
  • 深度学习与MPC融合：利用深度学习强大的感知和预测能力，提升MPC对复杂环境的理解和未来状态的预测精度。例如，可以使用神经网络预测交通参与者的意图和轨迹（如142中LLMs作为自动驾驶决策组件的研究方向），将其作为MPC的额外输入或转化为更准确的约束。同时，强化学习可以辅助MPC在特定场景下学习更优的控制策略，弥补模型缺陷。
  • 可变粒度MPC：根据场景的复杂程度和实时性要求，动态调整MPC的预测时域和控制频率。在简单、低风险场景下，可以采用较长的预测时域以获得更优的全局性能；在复杂、高风险场景下，则缩短预测时域并提高控制频率，以增强实时响应能力和安全性。

5.1.2 控制逻辑可解释性与透明度

在安全关键的自动驾驶系统中，仅仅实现高性能是不够的，还需要确保控制决策的可解释性和透明度，以便于故障诊断、责任追溯以及满足未来的法规要求。

  • “黑盒”问题：传统的MPC虽然基于显式模型和优化，但当模型变得非常复杂（如非线性MPC、大规模MPC）或与深度学习等“黑盒”技术结合时，其决策过程可能变得不透明。当车辆发生异常行为时，很难准确判断是模型预测错误、优化问题求解失败、约束冲突还是其他原因。
  • 信任与接受度：对于最终用户而言，理解自动驾驶系统为何做出某个决策是建立信任的关键。如果MPC的决策逻辑晦涩难懂，将可能影响公众对自动驾驶技术的接受度。
  • 法规与认证：未来的自动驾驶法规可能会要求控制系统具备一定程度的可解释性。例如，当发生事故时，系统需要能够提供清晰的证据，解释事故发生前车辆的决策依据和意图。这对于基于黑盒AI决策的系统是一个巨大挑战，而MPC由于其基于模型的特性，相对而言更容易提供这种解释。

应对方向：

  • MPC设计过程的透明化：确保MPC的预测模型、成本函数和约束条件都清晰、有据可循。在设计阶段，明确每个参数和权重的物理意义，并提供详细的文档。
  • 决策可视化与分析工具：开发先进的工具，实时或离线可视化MPC的预测轨迹、成本函数变化、约束满足情况以及优化变量的演变过程。这有助于工程师理解和调试MPC的行为，并在故障发生时进行根因分析。
  • 基于规则与逻辑的MPC集成：将人类专家知识和交通规则以逻辑和规则的形式嵌入到MPC中，例如，通过混合整数规划（MIP）或有限状态机（FSM）结合MPC，使决策过程更加符合人类直觉，并易于解释。143中提出的将决策制定和轨迹规划相结合的MPC方法，通过混合整数公式包含决策制定约束，并使用Sigmoid函数和制动屏障定义安全约束，使决策过程更具解释性。
  • 可解释AI与MPC结合：探索可解释AI（XAI）技术与MPC的结合。例如，利用XAI方法分析MPC的决策过程，识别影响决策的关键输入特征，并生成人类可理解的解释。

5.1.3 车规级硬件适配与高实时性要求

自动驾驶MPC的运行环境是车载嵌入式平台，其计算资源、功耗和散热都受到严格限制，但同时需要满足极高的实时性、可靠性和安全性要求。

  • 计算资源限制：车载计算平台（如域控制器、ECU）的CPU和GPU性能虽然不断提升，但相对于MPC在复杂场景下求解大规模非线性优化问题的计算需求而言，仍然是瓶颈。MPC的在线优化求解通常需要大量的矩阵运算和迭代，很难在有限的功耗和散热预算下实现毫秒级的循环周期。
  • 高可靠性与安全性：车规级硬件要求在极端环境下（温度、湿度、振动等）仍能稳定运行，并具备高安全等级（如ASIL D）认证。MPC软件在部署时需要经过严格的验证和测试，确保其在各种故障和异常情况下的行为符合安全规范。
  • 软件架构与集成：MPC需要与其他自动驾驶模块（感知、定位、规划、执行器）进行高效的数据交互和任务调度。如何将MPC无缝集成到复杂的车载软件架构中，并保证系统的整体实时性和稳定性，是一个巨大的工程挑战。

应对方向：

  • 端边轻量化MPC设计：如前文3.2节所述，通过模型裁剪、预测时域缩短、并行计算优化（利用GPU、FPGA加速）等手段，大幅降低MPC的计算复杂度。例如，27中通过GPU加速实现了随机MPC在RC模型车上的实时部署，证明了并行计算在提升MPC速度方面的潜力。144中提出了一种处理车辆纵向动态控制中复杂扭矩容量、换档引起的系统切换和多执行器系统等挑战的实用MPC方法。该方法采用约束局部仿射近似、车轮和执行器域分离以及燃油映射混合等技术，以最小的计算时间实现了准最优控制解，并且已在TuSimple的L4级卡车上进行了验证。
  • 定制化硬件加速器：针对MPC优化算法的特点，设计专用的硬件加速器（如FPGA或ASIC），将MPC的核心计算逻辑直接固化到硬件中，实现超高速计算，满足毫秒甚至微秒级响应的需求。
  • 软件框架优化：采用实时操作系统（RTOS）和针对车载环境优化的中间件，确保MPC模块能够获得稳定的计算资源和确定性的响应时间。利用形式化验证方法对MPC算法和软件实现进行验证，确保其正确性和安全性。
  • 工具链支持：开发或利用自动代码生成工具，将MPC设计模型直接转换为高效、可靠的车规级代码，减少手动编码错误，加速开发和部署周期。

5.1.4 法规、伦理与社会接受度

MPC在自动驾驶领域的应用还必须面对法规约束、伦理困境和社会接受度的考验。

  • 安全认证与法规遵循：各国政府正在制定自动驾驶的测试、验证和认证标准。MPC作为核心控制算法，需要证明其在所有可预见场景下的安全性和鲁棒性。例如，在不可避免的事故中，MPC需要遵循预先设定的伦理规则（如136中提出的Lexicographic Optimization-based MPC用于自动驾驶的伦理决策），这通常涉及牺牲最小伤害原则等复杂问题。
  • 伦理困境：自动驾驶汽车面临着“电车难题”等伦理困境，即在某些极端情况下，系统可能需要在不同损害结果之间做出选择。MPC如何编码和执行这些伦理决策，并确保决策过程的公平性和透明度，是巨大的挑战。136展示了LO-MPC在伦理决策方面的潜力。
  • 责任归属：当自动驾驶汽车发生事故时，责任归属是一个复杂的问题。MPC的决策过程需要有清晰的记录和解释，以帮助判断是制造商、软件供应商还是车辆所有者的责任。
  • 公众接受度：公众对自动驾驶技术的接受度取决于对其安全性和可靠性的信任。MPC在保障安全、提升舒适性方面的表现，直接影响公众对自动驾驶的信心。

应对方向：

  • 合规性设计与形式化验证：在MPC的设计之初就融入安全工程和形式化验证方法，确保算法满足安全标准（如ISO 26262）。通过数学证明MPC在特定条件下的稳定性和约束满足性，提升其可信度。
  • 伦理规则编码与透明化决策：与伦理学家、社会学者和政策制定者合作，将社会普遍接受的伦理原则以可计算的形式嵌入到MPC的决策逻辑中。同时，确保这些伦理决策的规则和依据对外部是透明和可审计的。
  • 事故数据记录与分析：部署强大的数据记录系统，详细记录MPC在事故发生前后的所有输入、内部状态和输出，为事故调查提供全面的数据支持。
  • 人机共驾与渐进式推广：在初期阶段，采用人机共驾模式，允许驾驶员在必要时接管车辆，逐步提升公众对自动驾驶的信任。同时，在特定受控区域（如园区、特定车道）进行试点运营，逐步扩大应用范围，降低社会风险。

综上所述，自动驾驶领域的MPC产业化落地是一个涉及技术创新、工程实践、社会伦理和法规建设的系统工程。克服这些挑战需要跨学科的紧密合作和持续的研发投入，才能最终实现安全、可靠、高效的自动驾驶愿景。

5.2 机器人领域MPC落地挑战

机器人领域对MPC的应用需求日益增长，尤其是在足式机器人、协作机器人和人形机器人等复杂系统中。MPC能够处理高自由度、非线性动力学和多约束问题，是实现这些机器人高级自主行为的关键技术。然而，MPC在机器人领域的产业化落地也面临着一系列独特的挑战，这些挑战主要源于机器人构型的多样性、部署成本的考量以及对动态非结构化环境的适应性需求。

5.2.1 不同构型机器人的MPC通用性问题

机器人的构型多种多样，从简单的轮式移动机器人到复杂的足式和人形机器人，它们在运动学、动力学特性以及应用场景上存在巨大差异。这导致为一种特定构型设计的MPC方案往往难以直接应用于其他构型，MPC的通用性成为一个核心挑战。

  • 模型差异性：MPC的核心是精确的预测模型。不同构型机器人拥有截然不同的运动学和动力学模型。例如，轮式机器人的运动学模型相对简单，而足式机器人则涉及复杂的接触动力学和全身平衡控制。人形机器人更是具有高自由度、多接触点和非完整约束等特点，其全身动力学模型异常复杂。为每一种机器人构型重新建立、辨识和验证MPC所需的精确模型，需要投入大量的时间和精力。
  • 约束多样性：不同机器人构型的操作约束也各不相同。机械臂有关节角度、速度、力矩限制；移动机器人则有速度、加速度、转弯半径限制；足式机器人则有接触力、摩擦锥、姿态稳定限制等。这些多样化的约束条件需要在MPC优化问题中进行精确表述，并针对特定构型进行定制化处理。
  • 优化目标差异性：不同机器人应用场景对优化目标的要求也不同。例如，工业机械臂可能更侧重于轨迹精度和节拍时间；服务机器人可能更注重安全性、舒适性和能耗；而特种机器人可能对鲁棒性和环境适应性有更高要求。这些差异化的优化目标需要MPC的成本函数进行定制化设计，并合理调整权重，这使得单一MPC框架难以满足所有构型和场景的需求。
  • 计算效率与实时性：高自由度机器人（如人形机器人）的MPC往往涉及大规模的非线性优化问题，其计算复杂度极高。例如，Marcucci等 提出的混合MPC算法，旨在处理机器人系统与环境交互的接触现象，虽然能通过在线凸优化实现，但面对人形机器人规模的复杂系统，实时计算仍是挑战 145。即便是足式机器人，Meduri等 提出的非线性MPC框架BiConMP，在实际四足机器人上生成各种循环步态并表现出色，其高效性也是通过高效利用机器人动力学结构实现的。如何设计一个既能适用于多种构型，又能满足实时性要求的MPC框架，是一个尚未完全解决的问题。

应对方向：

  • 参数化模型与自适应建模：开发参数化的MPC模型框架，允许通过调整少量参数来适应不同机器人构型。例如，可以基于通用机器人动力学方程，通过替换构型参数（如质量、惯量、关节长度等）来生成特定构型模型。此外，结合数据驱动和系统辨识技术，实现MPC模型的在线自适应调整，以应对模型不确定性或构型变化。
  • 分层与模块化MPC架构：设计分层MPC架构，将通用的高层任务规划与构型相关的低层运动控制分离。高层MPC负责通用决策和任务分解，而低层MPC则针对特定机器人构型进行优化。这种模块化设计可以提高MPC在不同机器人平台之间的复用性。
  • 统一的机器人软件框架：利用ROS (Robot Operating System) 等统一的机器人软件框架，为不同机器人构型提供标准化的接口和工具链，简化MPC算法的开发、集成和部署。

5.2.2 部署成本与技术门槛

MPC在机器人领域的部署成本不仅包括硬件投入，还涉及复杂的软件开发、系统集成和专业人才培养，这些都构成了其产业化落地的技术门槛。

  • 硬件成本：实现高性能MPC通常需要高精度的传感器（如激光雷达、视觉传感器、惯性测量单元）、大算力的嵌入式处理器或边缘计算设备。这些硬件设备的成本，尤其是在对功耗和体积有严格限制的场景下，可能会显著增加机器人的整体制造成本。
  • 软件开发与集成复杂性：MPC算法本身的设计和实现就具有较高的技术门槛，涉及到优化理论、数值计算、实时系统等多个领域的知识。此外，MPC需要与机器人的感知、状态估计、运动规划、故障诊断等多个模块进行紧密集成，这使得软件系统变得更加复杂，开发周期长，维护难度大。
  • 专业人才稀缺：MPC的开发、调试和维护需要具备深厚理论知识和丰富实践经验的工程师。目前，具备MPC专业技能的工程师在全球范围内相对稀缺，这限制了MPC在机器人领域的广泛应用和推广。
  • 模型构建与维护：MPC依赖于精确的系统模型。对于机器人而言，建立精确的动力学模型，尤其是在存在摩擦、弹性、接触不确定性等因素时，本身就是一项挑战。模型的辨识、验证以及后续的在线维护和更新，都需要专业知识和投入。例如，软机器人的控制面临模型构建困难的问题，Koopman算子理论提供了一种数据驱动的方法来构建显式动力学模型，并在此基础上设计MPC控制器，但这类方法的复杂性仍然存在 146。

应对方向：

  • MPC轻量化与高效求解器：持续研究和开发计算效率更高、资源占用更少的MPC算法和求解器。例如，利用显式MPC、算子拆分法（如ADMM）、以及硬件加速技术（如FPGA/ASIC）来降低在线计算的资源需求，使得MPC能够在更低成本的硬件平台上运行。文献中提到的Open框架利用PANOC和ALM技术实现了在嵌入式平台上极快的求解时间，为机器人臂的上下文感知（Context-aware）MPC提供了可能 147。
  • 低代码/无代码MPC开发工具：开发用户友好的MPC工具链和开发平台，提供图形化建模界面、自动化代码生成、仿真验证等功能，降低MPC的开发和部署难度，使更多非专业人士也能使用MPC。do-mpc等开源工具的出现正在朝着这个方向发展。
  • 模型库与知识共享：建立机器人通用模型库和MPC最佳实践知识库，降低新机器人平台MPC模型构建的门槛。推动学术界和工业界之间的合作与知识共享，加速MPC技术的普及。
  • 数据驱动建模与学习：利用机器学习技术辅助MPC模型的构建和自适应。例如，通过数据驱动方法学习机器人动力学参数，或利用强化学习进行模型修正，减少人工建模的工作量。

5.2.3 动态非结构化环境适应性弱

机器人通常需要在动态、非结构化的环境中执行任务，如家庭、仓库、户外等。MPC在这些复杂环境中面临的挑战包括感知不确定性、实时规划与避障以及对突发事件的响应能力。

  • 感知不确定性与时延：MPC的预测和优化依赖于准确的环境感知信息。在非结构化环境中，传感器数据可能受到噪声、遮挡、光照变化等因素的影响，导致感知结果不准确或存在时延。这些不确定性会降低MPC预测的准确性，进而影响控制决策的质量和安全性。
  • 实时动态避障能力不足：MPC虽然能够处理避障约束，但在动态、高度拥挤的非结构化环境中（如人流量大的公共场所），障碍物（特别是移动障碍物）的行为是不可预测的。MPC需要实时地预测多个动态障碍物的轨迹，并快速计算出无碰撞路径，这对于计算效率和算法鲁棒性是巨大的挑战。传统的基于静态环境假设的MPC难以应对这种情况。例如，Zhou等 提出的混合避障方法结合了RRT*和MPC，用于移动机器人在非结构化环境中的避障，能够考虑动态障碍物的运动方向和位置，但仍需在更复杂的场景中验证 148。
  • 对突发事件的响应：在非结构化环境中，机器人可能会遇到各种突发事件，如突然出现的障碍物、系统故障、外部干扰等。MPC需要在极短的时间内重新规划并调整控制策略，以确保机器人安全。然而，MPC的在线优化特性使其难以对完全未预见的突发事件做出即时、最优的响应。
  • 非线性、非凸优化问题：非结构化环境中的避障约束和动态行为往往是非线性和非凸的，这使得MPC优化问题更加难以实时求解。例如，Brito等 提出的用于非结构化动态环境中避碰的非线性MPCC方法，通过在线计算自由空间中的凸区域来处理这些问题，但计算负担依然存在。

应对方向：

  • 多模态感知融合与环境建模：融合激光雷达、相机、毫米波雷达等多种传感器数据，利用深度学习等技术提升环境感知和动态障碍物预测的准确性和鲁棒性。构建高精度的动态环境模型，为MPC提供更可靠的预测基础。
  • 分层与混合规划策略：结合高层（如基于图搜索的全局路径规划）和低层（如MPC实时轨迹优化）的规划方法，以平衡计算效率和决策质量。高层规划提供宏观路径，MPC则在局部负责精细化避障和轨迹跟踪。同时，融合启发式规则和机器学习模型，提升MPC在突发事件下的响应速度和决策智能性。
  • 鲁棒MPC与安全强化学习：采用鲁棒MPC设计方法，显式考虑感知和模型不确定性，确保机器人在不确定环境下的安全运行。结合安全强化学习（Safe Reinforcement Learning）技术，让机器人通过与环境的交互学习安全的控制策略，提高其在非结构化环境下的适应性，同时利用MPC等控制理论工具提供形式化的安全保证 34。
  • 实时非线性优化与近似解法：继续研究高效的实时非线性优化算法和近似MPC求解方法，以应对非结构化环境带来的非线性、非凸优化挑战。例如，采用基于梯度的优化方法、序列二次规划（SQP）以及专门为嵌入式系统设计的求解器等。

5.2.4 通用化框架设计与软硬件协同优化

为了克服上述挑战，机器人领域MPC的未来发展需要走向通用化框架设计与软硬件协同优化，以降低技术门槛、提升适应性和经济性。

  • 通用MPC框架：
    • 统一的模型表示：开发一种能够描述多种机器人构型的通用动力学模型表示方法（如多体动力学、广义坐标系），使得MPC算法可以在此统一模型基础上进行开发和复用。
    • 模块化组件库：构建丰富的MPC组件库，包括各种预测模型、成本函数模板、约束类型以及求解器接口。机器人开发者可以根据自身需求，通过组合和配置这些模块来快速构建MPC控制器。
    • 仿真与实物统一平台：提供一套从仿真到实物部署的统一工具链。在仿真环境中进行MPC算法的开发、测试和验证，然后通过自动代码生成等工具，无缝部署到实际机器人硬件上。
  • 软硬件协同优化：
    • 专用计算架构：针对MPC的计算特性，设计专用的边缘计算硬件，如集成高性能CPU、GPU、FPGA或DSP的异构处理器，甚至定制化的ASIC芯片，以提供高效率的并行计算能力，满足MPC的实时性需求。
    • 算法-硬件协同设计：在MPC算法设计阶段就考虑目标硬件的计算特性。例如，设计更适合并行化、流水线化的算法，充分利用硬件的并行处理能力。将MPC中的核心计算任务（如矩阵乘法、迭代求解）卸载到硬件加速器上，实现算力的最大化利用。
    • 弹性与异构调度：开发能够根据系统负载、可用资源和任务优先级动态调度MPC计算任务的运行时系统。在资源紧张时，可以自动切换到简化的MPC算法或降低控制频率，确保关键任务的执行。
    • 基于云边协同的MPC：将MPC的复杂优化计算（如模型训练、参数调优、大规模离线优化）放在云端，而将轻量化的在线控制律部署在边缘设备上。这种云边协同的架构可以平衡计算资源和实时性需求，同时利用云端大数据和AI能力持续优化边缘端的MPC性能。

通过通用化框架设计和软硬件协同优化，机器人领域的MPC有望突破当前面临的通用性、成本和环境适应性等瓶颈，从而加速其在工业、服务、医疗等更广泛领域的应用。这将推动机器人从传统的自动化工具向真正智能、自主、普适的平台发展。

5.3 工业过程控制领域MPC落地挑战

工业过程控制是MPC应用最成熟的领域，但其大规模、广范围的产业化落地仍面临诸多挑战。这些挑战主要体现在复杂工艺建模的高成本与精度难题、系统运维的知识壁垒，以及中小制造企业对MPC技术的接受度不足等方面。

5.3.1 复杂工艺建模成本与精度

MPC的核心是其预测模型。在复杂的工业过程中，建立一个既能准确反映系统动态，又能满足MPC实时优化需求的模型，是一项艰巨且成本高昂的任务。

  • 模型复杂性与非线性：许多工业过程，如化工反应、生物发酵、冶金过程等，具有显著的非线性、时变性、大滞后和强耦合特性。建立能够精确描述这些复杂动态的机理模型（第一性原理模型）需要深厚的领域知识、大量的实验数据和专业的建模工具，耗时耗力。即使是简化模型，也需要仔细平衡模型精度与计算复杂度。
  • 模型辨识与验证难度：当机理模型难以建立或过于复杂时，通常采用系统辨识方法来构建数据驱动模型（如ARX、FIR、神经网络模型）。然而，高质量的数据采集、去除噪声、有效激励输入的设计以及模型结构的选取和参数辨识，都需要专业的知识和经验。模型在不同工况下的适应性、准确性和鲁棒性也需要反复验证，这进一步增加了建模成本和周期。
  • 模型失配与维护：工业过程往往会随着设备老化、催化剂失活、原料变化、环境温度波动等因素发生动态变化，导致MPC赖以生存的预测模型出现失配。模型的在线更新和维护是一个持续性的挑战。不准确的模型会降低MPC的控制性能，甚至导致系统不稳定。
  • 多尺度与多物理场耦合：在某些先进制造过程中，如微电子制造、新材料制备，涉及多个物理场（热、流、力、电磁）的复杂耦合，以及从微观到宏观的多尺度动态。为这些过程构建统一且精确的MPC模型，几乎是一个“不可能完成的任务”。

应对方案：

  • 轻量化建模技术：
    • 基于数据驱动的简化模型：利用机器学习技术，通过少量关键数据快速构建轻量级的预测模型。例如，使用长短期记忆网络（LSTM）、门控循环单元（GRU）等深度学习模型捕捉非线性动态，或利用Koopman算子理论将非线性系统线性化，从而构建适合MPC的低维、线性化模型。这些方法可以在牺牲少量精度的前提下，大幅降低建模成本和计算复杂度。
    • 灰箱建模（Grey-Box Modeling）：结合有限的机理知识和大量的过程数据，构建混合模型。机理模型负责描述已知的物理化学规律，数据驱动模型则用于捕捉未知或难以建模的部分，如模型参数的不确定性或未建模动态。这可以在确保一定物理可解释性的同时，降低纯机理建模的难度。例如，在批次生产过程中，灰箱模型已被用于在线监测和预测产品质量，为MPC提供更精准的预测输入。
    • 模型降阶技术：对于复杂的高阶模型，采用平衡截断、模式分解等技术进行模型降阶，以获得低维的近似模型，从而减少MPC的计算负担。
  • 自动化模型辨识与维护平台：开发集成了数据清洗、特征工程、模型选择、参数辨识和性能评估等功能的自动化平台，降低对专业知识的依赖。同时，引入在线系统辨识和自适应更新机制，使MPC模型能够根据实时数据自动调整和优化，减少人工维护工作量，保持模型精度。
  • 领域知识与AI协同：将工业领域专家的经验知识（heuristics）融入到建模过程中，指导机器学习模型的特征选择、结构设计和结果解释。例如，在模型辨识中，专家可以帮助识别关键变量、确定滞后时间等，从而提高模型的有效性和可信度。

5.3.2 系统运维与知识壁垒

MPC系统的部署和持续运行需要专业的技能和知识，包括对MPC理论、优化算法、过程动态以及IT基础设施的理解，这构成了较高的知识壁垒。

  • 参数整定与优化：MPC的性能受到预测时域、控制时域、权重矩阵、约束参数等众多参数的影响。这些参数的整定需要丰富的经验和反复的实验，对于缺乏MPC专业知识的工厂工程师来说，是一个巨大的挑战。不当的参数设置可能导致控制性能不佳，甚至系统振荡或不稳定。
  • 故障诊断与处理：当MPC系统出现问题时（如性能下降、约束违反、优化器不收敛），诊断问题的根源（是模型问题、传感器故障、执行器问题还是算法问题）需要深入的专业知识。处理这些问题往往需要修改模型、调整参数或排查软件错误，对运维人员提出了更高的要求。
  • IT/OT融合挑战：MPC系统通常部署在工业控制网络（OT层）中，需要与DCS/PLC、SCADA系统进行数据交换。同时，为了实现远程监控、数据分析和云边协同，MPC也需要与企业IT网络（IT层）集成。IT和OT系统之间的安全隔离、数据协议转换、实时性保障等，都给系统运维带来了复杂性。
  • 安全与网络安全：随着工业控制系统与外部网络连接日益紧密，MPC系统也面临网络安全威胁。如何确保MPC系统的数据传输、算法运行和控制指令的安全性，防止恶意攻击或未授权访问，是一个不容忽视的挑战。

应对方案：

  • 低代码/无代码MPC开发工具链：
    • 可视化配置界面：提供直观的图形用户界面，允许工程师通过拖拽、配置参数的方式构建和部署MPC应用，而无需深入编写代码。例如，do-mpc等开源工具的开发，旨在降低MPC应用的技术门槛，简化模型定义、问题配置和结果分析。
    • 预定义模块与模板库：针对常见的工业过程（如加热、冷却、液位控制等），提供预构建的MPC模块和最佳实践模板。用户可以基于这些模板进行修改和定制，加速开发过程。
    • 自动化测试与验证：集成自动化测试工具，支持MPC算法的单元测试、集成测试和闭环仿真测试，确保系统在部署前的稳定性和可靠性。
  • 智能辅助决策与专家系统：
    • AI辅助参数整定：利用机器学习算法学习历史操作数据和专家经验，为MPC参数提供智能推荐或自动整定。例如，强化学习可以在仿真环境中自主学习最优参数策略。
    • 智能故障诊断系统：开发基于AI的故障诊断系统，结合历史故障数据和专家规则，实时监测MPC运行状态，自动识别潜在问题并提供诊断建议，甚至预测故障。
  • 强化培训与知识管理：为工业企业提供全面的MPC培训课程，培养具备MPC理论和实践能力的工程师。建立企业内部知识库，沉淀MPC应用的最佳实践、故障排除经验和参数整定指南。

5.3.3 中小制造企业接受度

尽管MPC在大型流程工业中应用广泛，但在广大中小制造企业中，其普及率仍然不高。这主要归因于成本敏感性、技术认知不足和投资回报率的不确定性。

  • 高昂的初始投入：中小企业通常资金有限，MPC系统的前期投入（包括软件许可、硬件采购、系统集成、人员培训等）对他们来说是一笔不小的开支。许多企业难以承担昂贵的MPC解决方案。
  • 技术认知与风险规避：中小企业对MPC等先进控制技术了解有限，对其潜在效益和风险缺乏清晰认知。他们可能更倾向于采用成熟、成本较低的传统控制方案，规避新技术带来的不确定性。
  • 投资回报率（ROI）评估困难：MPC的效益往往体现在提升生产效率、降低能耗、提高产品质量和减少停机时间等方面，这些效益的量化评估需要专业的工具和方法。中小企业可能缺乏能力准确评估MPC带来的投资回报率，从而难以做出投资决策。
  • 缺乏标准化解决方案：许多MPC解决方案是针对特定大型工业过程定制开发的，缺乏普适性和标准化。中小企业往往难以找到开箱即用、易于部署且价格合理的MPC产品。

应对方案：

  • 降低成本与简化部署：
    • 云端MPC服务（MPC as a Service）：将MPC作为一种云服务提供，中小企业可以按需订阅，无需承担高昂的初始投入和IT运维成本。云端MPC可以提供强大的计算资源和专业的运维支持。
    • 开源MPC工具与社区支持：推广和发展开源MPC工具（如do-mpc），降低软件成本。建立活跃的开源社区，提供技术支持和知识共享，帮助中小企业克服技术障碍。
    • 低成本硬件平台：利用如Raspberry Pi等低成本硬件（如中展示的，PLC与Raspberry Pi结合的控制平台）作为MPC的部署平台，大幅降低硬件成本。
    • 模块化、可配置的标准化产品：开发针对中小企业特点的、模块化、可配置的标准化MPC产品。这些产品可以针对常见工业设备（如PID控制器常用的泵、风机、阀门等）提供预设的MPC模块，降低定制化需求。
  • 提升技术认知与示范效应：
    • 成功案例推广：通过行业协会、政府机构等平台，广泛宣传MPC在中小企业中的成功应用案例，量化其带来的经济效益和管理提升，建立示范效应。
    • 政策扶持与补贴：政府可以出台相关政策，为中小企业引入先进控制技术提供资金补贴、税收优惠或技术咨询服务，降低其转型升级的门槛。
    • 产学研合作：鼓励中小企业与高校、科研机构进行产学研合作，共同开发和推广适合其需求的MPC解决方案，并进行技术转移和人才培养。
  • 清晰的价值主张与ROI量化：
    • 提供易于理解的价值主张：清晰阐述MPC如何帮助中小企业解决实际痛点（如产品合格率低、能耗高、操作不稳定等），并提供直观的效益分析。
    • ROI评估工具：开发简单易用的ROI评估工具，帮助中小企业快速估算投资MPC可能带来的经济效益，辅助决策。

通过上述应对策略，工业过程控制领域的MPC有望突破现有的产业化瓶颈，从大型流程工业逐步渗透到更广泛的中小制造企业，从而推动整个工业界迈向更智能、更高效的自动化生产。

6. MPC跨领域融合发展趋势预判

模型预测控制（MPC）在自动驾驶、机器人和工业过程控制领域的广泛应用已证明其作为先进控制范式不可替代的价值。展望未来5-10年，MPC将不再是孤立的技术，而是与其他前沿技术深度融合，形成新的发展趋势，以应对更复杂、更智能、更自主的应用需求。这种跨领域融合将主要体现在多模态感知融合MPC、大模型辅助MPC自适应调参以及云边端协同分布式MPC等方向。

6.1 多模态感知融合MPC

当前，MPC的性能高度依赖于对系统状态和环境信息的准确感知。单一模态的传感器（如摄像头、雷达、Lidar）往往存在局限性，例如摄像头易受光照和天气影响，雷达空间分辨率低，Lidar在恶劣天气下性能下降。多模态感知融合通过整合来自不同传感器的信息，能够提供更全面、更鲁棒的环境理解和状态估计，为MPC提供更可靠的输入。

  • 技术潜力：
    • 提升环境理解与预测精度：MPC的预测模型将从静态或简化的环境假设转向动态、高置信度的环境感知。例如，在自动驾驶中，融合视觉、雷达、激光雷达数据，可以更精确地识别车辆、行人、车道线，并预测其未来运动轨迹，从而使MPC在轨迹规划和碰撞避免时有更准确的依据。在机器人领域，多模态感知可以帮助机器人更好地理解复杂的工作空间，识别物体姿态，预测人机交互意图，从而实现更流畅、安全的协作。
    • 增强鲁棒性与抗干扰能力：当某一种传感器失效或受限时，其他模态的传感器可以提供补充信息，确保MPC仍能获得足够的决策依据。例如，在浓雾天气下，Lidar和摄像头可能受限，但毫米波雷达仍能提供距离和速度信息，保障自动驾驶MPC的基本功能。
    • 支撑复杂任务决策：多模态感知融合不仅提供原始数据，更重要的是能够生成高层次的语义信息（如路况分析、物体类别、场景意图等），这些信息可以直接作为MPC决策层的输入，使得MPC能够处理更复杂的任务，例如自动驾驶中的复杂路口博弈、机器人与人类的自然语言交互等。
  • 代表性研究与挑战：
    • 目前多模态感知融合的研究主要集中在感知层面，如深度学习在多传感器融合中的应用，但如何有效地将融合后的高维、不确定性信息无缝集成到MPC的优化框架中，仍是挑战。这需要MPC设计能够处理非结构化、高维输入的感知信息，并将其转化为可量化的成本函数或约束条件。
    • 将动态感知模型（如基于RNN或Transformer的预测模型）与MPC的预测时域耦合，实现端到端的“感知-预测-控制”一体化。
  • 落地节奏与应用拓展：
    • 近期（2-3年）：多模态感知融合MPC将在自动驾驶的L2+级辅助驾驶系统中逐步落地，提升高速公路辅助驾驶、城市拥堵跟车等场景的可靠性。在工业机器人领域，辅助机器人完成装配、检测等对感知精度要求高的任务。
    • 中期（4-6年）：随着技术成熟，将拓展到L3/L4级自动驾驶，处理更复杂的城市交通环境；在服务机器人领域，实现机器人对家庭或公共场所的更深层次理解和自主导航与交互。
    • 远期（7-10年）：赋能L5级全自动驾驶，机器人能够自主应对所有驾驶场景；工业过程控制领域，实现对复杂生产环境的全面感知和自适应控制，例如，通过视觉和触觉融合，精确控制柔性材料加工过程。

6.2 大模型辅助MPC自适应调参

传统MPC的性能对参数（如预测时域、控制时域、权重矩阵、约束裕度等）的整定非常敏感，而这些参数的调优通常依赖专家经验和反复试错，效率低下且难以适应动态变化的环境。大型语言模型（LLM）等大模型在理解、推理和生成方面的强大能力，为MPC的自适应调参带来了革命性机遇。

  • 技术潜力：
    • 智能参数整定与优化：大模型可以学习海量的历史运行数据、专家调参策略、甚至MPC的设计文档，从而理解不同工况下MPC参数对性能的影响。通过自然语言指令或高层目标设定，大模型可以智能地推荐或直接生成最优的MPC参数配置。例如，在化工过程中，针对不同的原料批次或产品规格，大模型可以辅助MPC调整反应器温度、压力等控制参数的权重，以最大化产量或降低能耗。
    • 故障诊断与自适应重构：当系统出现故障或模型失配时，大模型可以根据异常数据和预定义的知识库，辅助诊断故障原因，并建议MPC的参数调整策略或模型重构方案。例如，在自动驾驶车辆发生轻微碰撞后，大模型可以分析传感器数据和车辆状态，建议MPC调整避障参数或切换到更保守的驾驶模式。
    • 可解释性与人机交互：大模型能够将复杂的MPC决策过程进行解释，以人类可理解的语言说明MPC为何做出某个决策，以及当前参数配置的依据。这对于提升MPC的透明度和用户信任度至关重要，也有助于降低MPC系统的运维门槛。
  • 代表性研究与挑战：
    • 目前，大模型在控制领域的研究尚处于早期阶段，主要集中在利用大模型进行高层规划或决策。如何将大模型的推理能力与MPC的底层优化紧密结合，形成端到端的自适应调参闭环，仍需深入探索。
    • 数据隐私和计算资源是制约大模型在工业控制领域应用的挑战。联邦学习等技术（如149150151所述）在保护数据隐私的前提下，能够实现模型的协同训练，这为大模型在工业场景的应用提供了潜在的解决方案。
  • 落地节奏与应用拓展：
    • 近期（2-3年）：大模型将作为辅助工具，帮助工程师进行MPC参数的初步整定和优化建议，或在特定工况下提供参数调整的指导。
    • 中期（4-6年）：通过强化学习与大模型的结合，实现MPC参数的在线自适应调整，使其能够响应环境变化。在自动驾驶中，辅助MPC在不同交通流和天气条件下，自适应调整驾驶风格。
    • 远期（7-10年）：实现全自动的“自优化MPC”，大模型能够完全自主地学习、调优和管理MPC参数，甚至在系统设计阶段辅助MPC模型的构建和验证，大幅降低MPC的部署和运维成本。

6.3 云边端协同分布式MPC

随着工业物联网（IIoT）、边缘计算和5G通信技术的发展，大规模、地理分散的系统（如智能电网、智慧城市交通、大型智能工厂）对分布式控制的需求日益迫切。云边端协同架构为分布式MPC提供了强大的计算和通信支撑。

  • 技术潜力：
    • 提升系统可扩展性与鲁棒性：将MPC任务分解到边缘端和云端执行，可以有效降低单个控制器的计算负担，提升系统整体的可扩展性。边缘端MPC负责局部快速响应和低延迟控制，云端则负责全局优化、长期规划和复杂数据分析。即使部分边缘节点失效，系统也能通过云端或邻近边缘节点进行协调，增强鲁棒性。
    • 优化资源利用与降低通信延迟：边缘计算可以在数据源头附近进行局部MPC优化，减少数据上传到云端的通信开销和延迟，这对于自动驾驶车辆编队、多机器人协作等需要毫秒级响应的应用至关重要。例如，分布式MPC已成功应用于多机器人运动规划中，通过事件触发的策略，实现了高效的协同避障和路径生成152。
    • 数据驱动与集中学习：边缘设备可以持续收集本地数据，并在本地进行初步处理和MPC优化。同时，这些数据或其提取的特征可以匿名化后上传到云端，用于训练大模型或进行全局优化，从而实现 MPC 模型和参数的持续改进。这种云边端的协同学习模式与联邦学习的理念不谋而合，能在保护隐私的前提下提升整体系统的智能化水平149150151。
    • 能耗与碳排放优化：在能源管理领域，云边端协同分布式MPC能够实时监测和优化整个区域的能源生产、存储和消费，例如，通过协调微电网中的多个分布式能源设备，实现能源的高效利用和碳排放的最小化。例如，对并网风光微电网的协调优化运行MPC策略，其中包含了混合储能管理系统，旨在延长储能设备的寿命并管理电力和氢气的生产。
  • 代表性研究与挑战：
    • 分布式MPC的协调机制、通信延迟与丢包对稳定性的影响、以及子系统分解策略的通用性仍是研究热点。
    • 如何有效地在云端、边缘端和终端设备之间分配MPC的计算任务和数据流，确保实时性、安全性和隐私性，是云边端协同架构面临的关键挑战。
  • 落地节奏与应用拓展：
    • 近期（2-3年）：在大型智能工厂中，分布式MPC将用于协调多个生产线或子系统，优化整体生产效率。在智能交通领域，应用于区域交通信号灯控制和车队管理。
    • 中期（4-6年）：自动驾驶车队中的云边端协同MPC将实现更高效、安全的编队行驶和协同避障。智慧城市中的分布式能源管理和微电网优化将得到更广泛的应用。
    • 远期（7-10年）：实现真正意义上的“智能自治系统”，如无人驾驶的智慧城市交通系统，多个分布式MPC系统在云边端架构下无缝协作，动态适应城市运行状态，提供高效、安全的交通服务。工业过程控制将全面实现云边端协同，实现全厂级的自优化和柔性生产。

总而言之，未来MPC的发展将是一个跨学科、多技术融合的进程。多模态感知将为MPC提供更精准的环境洞察，大模型将赋能MPC更智能的自适应能力，而云边端协同架构则将扩展MPC的应用范围和规模。这三大趋势将共同推动MPC在自动驾驶、机器人和工业过程控制等领域实现更高水平的自主性、智能化和鲁棒性，从而在未来5-10年内，深刻改变我们的生产和生活方式。

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参考文献

1Model Predictive Control for Power Converters and Drives: Advances and TrendsOpenAlex

Sergio Vázquez, José Rodríguez, Marco Rivera, et al.
Model predictive control (MPC) is a very attractive solution for controlling power electronic converters. The aim of this paper is to present and discuss the latest developments in MPC for power converters and drives, describing the current state of this control strategy and analyzing the new trends and challenges it presents when applied to power electronic systems. The paper revisits the operating principle of MPC and identifies three key elements in the MPC strategies, namely the prediction model, the cost function, and the optimization algorithm. This paper summarizes the most recent research concerning these elements, providing details about the different solutions proposed by the academic and industrial communities.

2Model Predictive ControlOpenAlex

Biao Huang, Yutong Qi, AKM Monjur Murshed
This chapter contains sections titled: Model Predictive Control: State-of-the-Art General Principle Dynamic Matrix Control Nonlinear MPC General Tuning Guideline of Nonlinear MPC Discretisation of Models: Orthogonal Collocation Method Pros and Cons of MPC Optimisation Example: Chaotic System Notes and References

3An Introduction to Nonlinear Model Predictive ControlOpenAlex

Rolf Findeisen, Frank Allgöwer
While linear model predictive control is popular since the 70s of the past century, the 90s have witnessed a steadily increasing attention from control theoretists as well as control practitioners in the area of nonlinear model predictive control (NMPC). The practical interest is driven by the fact that today’s processes need to be operated under tighter performance specifications. At the same time more and more constraints, stemming for example from environmental and safety considerations, need to be satisfied. Often these demands can only be met when process nonlinearities and constraints are explicitly considered in the controller. Nonlinear predictive control, the extension of well established linear predictive control to the nonlinear world, appears to be a well suited approach for this kind of problems. In this note the basic principle of NMPC is reviewed, the key advantages/disadvantages of NMPC are outlined and some of the theoretical, computational, and implementational aspects of NMPC are discussed. Furthermore, some of the currently open questions in the area of NMPC are outlined. 1 Principles, Mathematical Formulation and Properties of Nonlinear Model Predictive Control Model predictive control (MPC), also referred to as moving horizon control or receding horizon control, has become an attractive feedback strategy, especially for linear processes. Linear MPC refers to a family of MPC schemes in which linear models are used to predict the system dynamics, even though the dynamics of the closed-loop system is nonlinear due to the presence of constraints. Linear MPC approaches have found successful applications, especially in the process industries. A good overview of industrial linear MPC techniques can be found in [64, 65], where more than 2200 applications in a very wide range from chemicals to aerospace industries are summarized. By now, linear MPC theory is quite mature. Important issues such as online computation, the interplay between modeling/identification and control and system theoretic issues like stability are well addressed [41, 52, 58]. Many systems are, however, in general inherently nonlinear. This, together with higher product quality specifications and increasing productivity demands, tighter environmental regulations and demanding economical considerations in the process industry require to operate systems closer to the boundary of the admissible operating region. In these cases, linear models are often inadequate to describe the process dynamics and nonlinear models have to be used. This motivates the use of nonlinear model predictive control. This paper focuses on the application of model predictive control techniques to nonlinear systems. It provides a review of the main principles underlying NMPC and outlines the key advantages/disadvantages of NMPC and some of the theoretical, computational, and implementational aspects. Note, however, that it is not intended as a complete review of existing NMPC techniques. Instead we refer to the following list for some excellent reviews [4, 16, 22, 52, 58, 68]. In Section 1.1 and Section 1.2 the basic underlying concept of NMPC is introduced. In Section 2 some of the system theoretical aspects of NMPC are presented. After an outline of NMPC schemes that achieve stability one particular NMPC formulation, namely quasi-infinite horizon NMPC (QIH-NMPC) is outlined to exemplify the basic ideas to achieve stability. This approach allows a (computationally) efficient formulation of NMPC while guaranteeing stability and performance of the closed-loop. Besides the basic question of the stability of the closed-loop, questions such as robust formulations of NMPC and some remarks on the performance of the closed-loop are given in Section 2.3 and Section 2.2. Section 2.4 gives some remarks on the output-feedback problem in connection with NMPC. After a short review of existing approaches one

4An Online Optimal Dispatch Schedule for CCHP Microgrids Based on Model Predictive ControlOpenAlex

Wei Gu, Zhihe Wang, Zhi Wu, et al.
Combined cooling, heating, and power (CCHP) systems have been widely applied in various kinds of buildings. Most operation strategies for CCHP microgrids are designed based on day-ahead profiles. However, prediction error for renewable energy resources (RES) and load leads to suboptimal operation in dispatch scheduling. In this paper, we propose an online optimal operation approach for CCHP microgrids based on model predictive control with feedback correction to compensate for prediction error. This approach includes two hierarchies: 1) rolling optimization; and 2) feedback correction. In the rolling part, a hybrid algorithm based on integrating time series analysis and Kalman filters is used to forecast the power for RES and load. A rolling optimization model is established to schedule operation according to the latest forecast information. The rolling dispatch scheduling is then adjusted based on ultra-short-term error prediction. The feedback correction model is applied to minimize the adjustments and to compensate for prediction error. A case study demonstrates the effectiveness of the proposed approach with better matching between demand and supply.

5MPC and PID control based on Multi-Objective OptimizationOpenAlex

Adrian Gambier
The design of sophisticated control systems have led in the past ten years to the necessity of satisfying more than one design criterion. Thus, it is natural to think that those criteria can be met in an optimal manner. If several criteria have simultaneously to be optimized, one is in presence of a multi-objective optimization problem. In this paper, many efforts to design the most popular control strategies, i.e. PID and MPC, by using multi-objective optimization techniques are reviewed. Both control strategies have dissimilar optimization characteristics and therefore, they can be considered as representative of two different multi-objective optimization problems, which are described including definitions, possible solutions, algorithms and available software implementations.

6An Online Energy Management System for a Grid-Connected Hybrid Energy SourceOpenAlex

Mohamed S. Taha, Hussein Abdeltawab, Yasser Abdel‐Rady I. Mohamed
An online energy management system (EMS) for a grid-connected hybrid energy source is proposed in this paper. The hybrid source combines renewable energy resources (wind and photovoltaic), battery storage, variable speed diesel generator, and load management system. The proposed EMS consists of two-level optimization algorithm: 1) the rolling optimization and 2) the feedback intrasample correction. The rolling optimization part is established to schedule operation based on the forecast data using the model-predictive control approach. The rolling dispatch scheduling is then adjusted based on an intrasample feedback correction that compensates for the prediction error of the forecast data. The optimization problem was formulated as mixed-integer linear programming framework with two objectives: 1) to minimize the total operating cost and 2) to minimize the pollutant gas emissions. The battery daily number of cycles and the minimum state of charge are considered as decision variables that are optimally determined by the EMS to minimize the total system operating cost while considering all the practical constraints of the different energy sources. Different case studies with different market profiles demonstrate the effectiveness of the proposed approach, and the results have showed a significant reduction in the total system cost.

7Multitime-Scale Optimal Dispatch of Railway FTPSS Based on Model Predictive ControlOpenAlex

Minwu Chen, Zhe Cheng, Yuanli Liu, et al.
The flexible traction power supply system (FTPSS) integrates back-to-back converter, and hybrid energy storage system (HESS) and photovoltaic (PV) generation system will be an important part of the smart railway. The FTPSS not only cancels the neutral zone but also facilitates the utilization of regenerative braking (RB) and renewable energy, but the random fluctuation of PV and the sudden change of traction load will exert influence on the safe and efficient operation of the FTPSS. To improve the benefits of FTPSS and compensate for the imbalance between supply and demand in short-term operation, a multitime-scale optimal dispatch method is proposed for flexible railway energy management (FREM), which integrates day-ahead dispatch and intraday feedback correction. During the day-ahead dispatch, the minimizing operating costs problem is formulated as a mixed linear programming model by coordination between HESS, RB, and PV output. For intraday energy adjustment dispatch, a rolling optimization based on model predictive control combined with the feedback correction method is proposed, with aim of minimum operation deviation of FTPSS because of adjusting the HESS dispatch plan drew up at day-ahead. Finally, the effectiveness of the proposed FREM control strategy is verified by the detailed real case study of a railway line in China.

8Adaptive and Predictive Energy Management Strategy for Real-Time Optimal Power Dispatch From VPPs Integrated With Renewable Energy and Energy StorageOpenAlex

Ghulam Mohy‐ud‐din, Kashem M. Muttaqi, Danny Sutanto
Virtual power plants (VPPs) have become a driving force for the decentralized energy industry, due to their efficient management and control of distributed energy resources. Most of the operation strategies for VPPs are designed based on the day-ahead forecasts. However, the prediction errors of the renewable energy sources (RES) and loads in the power dispatch schedule can lead to a suboptimal operation. In this article, an adaptive and predictive energy management strategy for a real-time optimal operation of VPPs is proposed based on the model predictive control technique with a feedback correction (FC) to compensate for the prediction error. This strategy has two parts: 1) receding-horizon optimization (RHO), and 2) FC. In the first part, a hybrid prediction algorithm based on the integration of the time-series model and the Kalman filter is used to forecast the output powers of RES and the loads. Based on the prediction, the RHO model schedules the operation following the latest forecast information. In the second part, the receding schedule is adjusted based on the fast-rolling gray model's ultrashort-term error prediction. The FC is applied to minimize the adjustments for compensating the prediction error. The proposed strategy is implemented on a VPP in a real electricity distribution system in New South Wales, Australia. The simulation results demonstrate the effectiveness of the proposed strategy with a better tracking of the actual available resources and a minimal mismatch between demand and supply.

9A New Active Fault Tolerant Control System: Predictive Online Fault EstimationOpenAlex

Robab Ebrahimi Bavili, Ardashir Mohammadzadeh, Jafar Tavoosi, et al.
This study presents a new approach for active fault-tolerant controller (FTC) design for constrained nonlinear multi-variable systems. The proposed approach utilize the nonlinear model predictive controller (NMPC) and fault estimation method which is on basis of extended kalman filters (EKFs). The deficiency of actuators and sensors and also the plant states measurement errors are estimated by the suggested approach. A supervisor unit using the fault information and fault modeling per sampling time, corrects the predictor model of the controller and compensates actuator and sensor faults in control system. Furthermore, by the presented feedback compensation, the robustness of the designed method against plant faults and uncertainties is ensured. The important advantages of the proposed method are: (1) The suggested FTC scheme based on NMPC leads to calculate more accurate control action than MPC in nonlinear processes, (2) it is comprehensive in fault accommodation point of view because it is able to compensate all types of faults in control systems simultaneously, (3) it has low computational cost because of using NMPC by analytical solution, (4) it can handle control and states constraints to prevent of actuator saturations and unsafe situations, (5) the simplicity and effectiveness of the designed FTC scheme for real applications is more significant. Simulation results on continuous stirred tank reactor process verifies the superiority and capability of the designed approach.

10Wiener model identification and predictive control of a pH neutralisation processOpenAlex

Juan Carlos Gómez, Arthur Jutan, Enrique Baeyens
Wiener model identification and predictive control of a pH neutralisation process is presented. Input-output data from a nonlinear, first principles simulation model of the pH neutralisation process are used for subspace-based identification of a black-box Wiener-type model. The proposed nonlinear subspace identification method has the advantage of delivering a Wiener model in a format which is suitable for its use in a standard linear-model-based predictive control scheme. The identified Wiener model is used as the internal model in a model predictive controller (MPC) which is used to control the nonlinear white-box simulation model. To account for the unmeasurable disturbance, a nonlinear observer is proposed. The performance of the Wiener model predictive control (WMPC) is compared with that of a linear MPC, and with a more traditional feedback control, namely a PID control. Simulation results show that the WMPC outperforms the linear MPC and the PID controllers.

11Robust decentralized model predictive control approach for a multi-compressor system surge instability including piping acousticOpenAlex

Hashem Imani Marrani, Mohammad Reza Jahed‐Motlagh, Karim Salahshoor, et al.
One of the major problems in modern gas compressing stations is related to surge control of compression system with multi-compressor. Due to the coupled system dynamics, standard controllers can interfere with each unit′s performance. This article introduces a new robust decentralized model predictive control (MPC) scheme for a team of cooperating compressors. In the decentralized control strategy, the integration of H∞ control scheme into a robust tube MPC algorithm is used to solve the surge problem of a multi-compressor dynamical process subject to constraints in a computation efficient way. Nonlinear dynamic for each compressor that contains acoustic of compressor system is considered and brings up the effects of the station’s piping system on the compressor surge Numerical simulations approve the capability of the proposed surge control method and guaranty the asymptotic stability of compression system in the presence of disturbances and coupling effects.

12Dynamic Positioning With Model Predictive ControlOpenAlex

Aleksander Veksler, Tor Arne Johansen, Francesco Borrelli, et al.
Marine vessels with dynamic positioning (DP) capability are typically equipped with sufficient number of thrusters to make them overactuated and with satellite navigation and other sensors to determine their position, heading, and velocity. An automatic control system is tasked with coordinating the thrusters to move the vessel in any desired direction and to counteract the environmental forces. The design of this control system is usually separated into several levels. First, a DP control algorithm calculates the total force and moment of force that the thruster system should produce. Then, a thrust allocation (TA) algorithm coordinates the thrusters so that the resultant force they produce matches the request from the DP control algorithm. Unless significant heuristic modifications are made, the DP control algorithm has limited information about the thruster effects such as saturations and limited rate of rotation of variable-direction thrusters, as well as systemic effects such as singular thruster configurations. The control output produced with this control architecture is therefore not always optimal, and may result in a position loss that would not have occurred with a more sophisticated control algorithm. Recent advances in computer hardware and algorithms make it possible to consider a model-predictive control (MPC) algorithm that combines positioning control and TA into a single algorithm, which should theoretically yield a near-optimal controller output. This paper explores the advantages and disadvantages of using MPC compared with the traditional algorithms.

13A real time multi-objective optimization Guided-MPC strategy for power-split hybrid electric bus based on velocity predictionOpenAlex

Dongpo Yang, Tong Liu, Dafeng Song, et al.

14Bi-level dispatch and control strategy based on model predictive control for community integrated energy system considering dynamic response performanceOpenAlex

Chunming Liu, Chunling Wang, Yujun Yin, et al.

15Balancing CO<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg" display="inline" id="d1e1240"><mml:msub><mml:mrow/><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> emissions and economic cost in a microgrid through an energy management system using MPC and multi-objective optimizationOpenAlex

Luis O. Polanco Vásquez, Juana L. Redondo, J.D. Álvarez, et al.

16A P-Q Coordination Based Model Predictive Control for DFIG High-Voltage Ride ThroughOpenAlex

Changping Zhou, Zhen Wang, Huanhai Xin, et al.
This paper presents a P-Q coordination based model predictive control (MPC) for doubly fed induction generator (DFIG) to handle high-voltage ride through (HVRT) considering bipolar blocking of high-voltage direct current (HVDC) system. The overvoltage at the point of common coupling (PCC) after DC bipolar blocking and its sensitivity to current injection of DFIG is firstly analyzed based on a typical sending-end AC grid equivalent model. Then, the current feasible region of DFIG operation during overvoltage process is explicitly revealed considering generator and converter constrains. In the proposed HVRT control, a model predictive control (MPC) based method is developed where the minimum voltage tracking error is taken as the main objective function and the constrains are updated every control horizon based on real-time current feasible region. Through the rolling optimization and feedback correction framework, the rotor active and reactive currents of DFIG are coordinated and PCC voltage can be finally controlled to its target value to achieve HVRT. Further, the key MPC parameters are determined by solving an optimal problem to achieve better system robust stability and dynamic performances. Finally, the validity of the proposed control is verified by simulations in MATLAB/Simulink.

17Demand reduction in building energy systems based on economic model predictive controlOpenAlex

Jingran Ma, S. Joe Qin, Timothy I. Salsbury, et al.

18A bi-level optimization strategy for flexible and economic operation of the CHP units based on reinforcement learning and multi-objective MPCOpenAlex

Keyan Zhu, Guangming Zhang, Zhu Chen, et al.

19Model Predictive Control: Design and implementation using MATLAB (T-3)OpenAlex

Liuping Wang
Model Predictive Control (MPC) has a long history in the field of control engineering. It is one of the few areas that have received on-going interest from researchers in both the industrial and academic communities. Three major aspects of model predictive control make the design methodology attractive to both engineers and academics. The first aspect is the design formulation, which uses a completely multivariable system framework where the performance parameters of the multivariable control system are related to the engineering aspects of the system; hence, they can be understood and ‘tuned’ by engineers. The second aspect is the ability of method to handle both ‘soft’ constraints and hard constraints in a multivariable control framework. This is particularly attractive to industry where tight profit margins and limits on the process operation are inevitably present. The third aspect is the ability to perform process on-line optimization.

20A robust nonlinear model predictive controller for a multiscale thin film deposition processOpenAlex

Shabnam Rasoulian, Luis Ricardez‐Sandoval

21RTO: An overview and assessment of current practiceOpenAlex

Mark L. Darby, Michael Nikolaou, James Jones, et al.

22Application of a grey-box modelling approach for the online monitoring of batch production in the chemical industryOpenAlex

Ala Eldin Bouaswaig, Keivan Rahimi‐Adli, Matthias Roth, et al.
Abstract Model-based solutions for monitoring and control of chemical batch processes have been of interest in research for many decades. However, unlike in continuous processes, in which model-based tools such as Model Predictive Control (MPC) have become a standard in the industry, the reported use of models for batch processes, either for monitoring or control, is rather scarce. This limited use is attributed partly to the inherent complexity of the batch processes (e. g., dynamic, nonlinear, multipurpose) and partly to the lack of appropriate commercial tools in the past. In recent years, algorithms and commercial tools for model-based monitoring and control of batch processes have become more mature and in the era of Industry 4.0 and digitalization they are slowly but steadily gaining more interest in real-word batch applications. This contribution provides a practical example in this application field. Specifically, the use of a grey-box modeling approach, in which a multiway Projection to Latent Structure (PLS) model is combined with a first-principles model, to monitor the evolution of a batch polymerization process and predict in real-time the final batch quality is reported. The modeling approach is described, and the experimental results obtained from an industrial batch laboratory reactor are presented.

23Distribution control of particulate systems based on population balance equation modelsOpenAlex

Michael A. Henson
Manufacturing processes in which the desired product takes the form of individual particles are ubiquitous in the chemical, pharmaceutical and agricultural industries. Particulate processes often are modeled using a form of the population balance equation (PBE) which describes the evolution of the particle distribution. In many applications, control of the particle distribution is necessary to achieve the desired product properties. In this paper, a model predictive control strategy based on a discretized representation of a general one-dimensional PBE is proposed for particle distribution control. The controller is formulated to minimize the least squares difference between the predicted and target distribution measurements. The proposed method is applied to the problem of cell mass distribution control in a continuous yeast fermentor.

24Model Predictive Control for Autonomous and Semiautonomous VehiclesOpenAlex

Yiqi Gao
In this thesis we consider the problem of designing and implementing Model Predictive Controllers (MPC) for lane keeping and obstacle avoidance of autonomous or semi-autonomous ground vehicles. Vehicle nonlinear dynamics, fast sampling time and limited computational resources of embedded automotive hardware make it a challenging control design problem. MPC is chosen because of its capability of systematically taking into account nonlinearities, future predictions and operating constraints during the control design stage.We start from comparing two different MPC based control architectures. With a given trajectory representing the driver intent, the controller has to autonomously avoid obstacles on the road while trying to track the desired trajectory by controlling front steering angle and differential braking. The first approach solves a single nonlinear MPC problem for both replanning and following of the obstacle free trajectories. While the second approach uses a hierarchical scheme. At the high-level, new trajectories are computed on-line, in a receding horizon fashion, based on a simplified point-mass vehicle model in order to avoid the obstacle. At the low-level an MPC controller computes the vehicle inputs in order to best follow the high level trajectory based on a higher fidelity nonlinear vehicle model. Experimental results of both approaches on icy roads are shown. The experimental as well as simulation results are used to compare the two approaches. We conclude that the hierarchical approach is more promising for real-time implementation and yields better performance due to its ability of having longer prediction horizon and faster sampling time at the same time. Based on the hierarchical approach for autonomous drive, we propose a hierarchical MPC framework for semi-autonomous obstacle avoidance, which decides the necessity of control intervention based on the aggressiveness of the evasive maneuver necessary to avoid collisions. The high level path planner plans obstacle avoiding maneuvers using a special kind of curve, the clothoid. The usage of clothoids have a long history in highway design and robotics control. By optimizing over a small number of parameters, the optimal clothoids satisfying the safety constraints can be determined. The same parameters also indicate the aggressiveness of the avoiding maneuver and thus can be used to decide whether a control intervention is needed before its too late to avoid the obstacle. In the case of control intervention, the low level MPC with a nonlinear vehicle model will follow the planned avoiding maneuver by taking over control of the steering and braking. The controller is validated by both simulations and experimental tests on an icy track.In the proposed autonomous hierarchical MPC where the point mass vehicle model is used for high level path replanning, despite of its successful avoidance of the obstacle, the controller's performance can be largely improved. In the test, we observed deviations of the actual vehicle trajectory from the high level planned path. This is because the point mass model is overly simplified and results in planned paths that are infeasible for the real vehicle to track. To address this problem, we propose an improved hierarchical MPC framework based on a special coordinate transformation in the high level MPC. The high level uses a nonlinear bicycle vehicle model and utilizes a coordinate transformation which uses vehicle position along a path as the independent variable. That produces high level planned paths with smaller tracking error for the real vehicle while maintaining real-time feasibility. The low level still uses an MPC with higher fidelity model to track the planned path. Simulations show the method's ability to safely avoid multiple obstacles while tracking the lane centerline. Experimental tests on an autonomous passenger vehicle driving at high speed on an icy track show the effectiveness of the approach.In the last part, we propose a robust control framework which systematically handles the system uncertainties, including the model mismatch, state estimation error, external disturbances and etc. The framework enforces robust constraint satisfaction under the presence of the aforementioned uncertainties. The actual system is modeled by a nominal system with an additive disturbance term which includes all the uncertainties. A "Tube-MPC" approach is used, where a robust control invariant set is used to contain all the possible tracking errors of the real system to the planned path (called the "nominal path"). Thus all the possible actual state trajectories in time lie in a tube centered at the nominal path. A nominal NMPC controls the tube center to ensure constraint satisfaction for the whole tube. A force-input nonlinear bicycle vehicle model is developed and used in the RNMPC control design. The robust invariant set of the error system (nominal system vs. real system) is computed based on the developed model, the associated uncertainties and a predefined disturbance feedback gain. The computed invariant set is used to tighten the constraints in the nominal NMPC to ensure robust constraint satisfaction. Simulations and experiments on a test vehicle show the effectiveness of the proposed framework.

25A Comparative Study of Stanley, LQR and MPC Controllers for Path Tracking Application (ADAS/AD)OpenAlex

K. Vivek, Milankumar Ambalal Sheta, Veershetty Gumtapure
This paper presents comparative study between Stanley, LQR (Linear Quadratic Regulator) and MPC (Model Predictive Controller) controllers for path tracking application, which is a level 4 automation feature under ADAS/AD (Advanced Driver Assistance System/Autonomous Driving). The accuracy associated with all the controllers are compared by making the vehicle model run in a prescribed environment. The initial designs are done in MATLAB environment and later they are interfaced with IPG CarMaker vehicle simulation tool for fine tuning. Stanley controller is more of an intuitive steering control law where as LQR and MPC are more advanced optimal controllers. The control actions are calculated by optimising the states of the model. Kinematic vehicle model is used with states as errors and a comparator design is made to find the deviation of the vehicle from the prescribed path. The paper gives a detailed idea about the controllers regarding its use, advantages and limitations in this application.

26Path Tracking Control for Autonomous Vehicles Based on an Improved MPCOpenAlex

Hengyang Wang, Biao Liu, Xianyao Ping, et al.
In this paper, an improved Model Predictive Control (MPC) controller based on fuzzy adaptive weight control is proposed to solve the problem of autonomous vehicle in the process of path tracking. The controller not only ensures the tracking accuracy, but also considers the vehicle dynamic stability in the process of tracking, i.e., the vehicle dynamics model is used as the controller model. Moreover, the problem of driving comfort caused by the application of classical MPC controller when the vehicle is deviated from the target path is solved. This controller is mainly realized by adaptively improving the weight of the cost function in the classical MPC through the fuzzy adaptive control algorithm. A comparative study which compares the proposed controller with the pure-pursuit controller and the classical MPC controller is made: through the CarSim-Matlab/Simulink co-simulations, the results show that this controller presents better tracking performance than the latter ones considering both tracking accuracy and steering smoothness.

27Real-Time Implementation of Randomized Model Predictive Control for Autonomous DrivingOpenAlex

Arun Muraleedharan, Hiroyuki Okuda, Tatsuya Suzuki
Model predictive control (MPC) using randomized optimization is expected to solve different control problems. However, it still faces various challenges for real-world applications. This paper attempts to solve those challenges and demonstrates a successful implementation of randomized MPC on the autonomous driving using a radio-controlled (RC) car. First of all, a sample generation technique in the frequency domain is discussed. This prevents undesirable randomness which affect the smoothness of the steering operation. Second, the proposed randomized MPC is implemented on a Graphics Processing Unit (GPU). The expected GPU acceleration in calculation speed at various problem sizes is also presented. The results show the improved control performance and computational speed that was not achievable using CPU based implementation. Besides, the selection of parameters for randomized MPC is discussed. The usefulness of the proposed scheme is demonstrated by both simulation and experiments. In the experiments, a 1/10 model RC car is used for collision avoidance task by autonomous driving.

28Event-Triggered Model Predictive Adaptive Dynamic Programming for Road Intersection Path Planning of Unmanned Ground VehicleOpenAlex

Chaofang Hu, Lingxue Zhao, Ge Qu
Autonomous driving of unmanned ground vehicle (UGV) at road intersection is a challenging task due to the complicated traffic conditions. In this paper, an event-triggered model predictive adaptive dynamic programming (MPADP) algorithm is proposed for path planning of UGV at road intersection. Following the critic-actor scheme of adaptive dynamic programming (ADP), cost function approximation and control policy generation are combined to formulate MPADP. The infinite horizon cost function of ADP is stacked over predictive horizon of model predictive control (MPC), and then the infinite horizon cost function is converted to the finite horizon-stacked cost function in MPADP. By minimizing the approximation error within predictive horizon, the approximation accuracy is enhanced. Considering the limitation of energy consumption, the event-triggered mechanism is designed based on the mismatch of cost function approximation. Three triggering conditions are designed, and the corresponding boundedness of approximation error is proved. Simulation results illustrate the effectiveness, efficiency and feasibility in application of the event-triggered MPADP method for path planning at road intersection.

29Surround Vehicle Motion Prediction Using LSTM-RNN for Motion Planning of Autonomous Vehicles at Multi-Lane Turn IntersectionsOpenAlex

Yonghwan Jeong, Seonwook Kim, Kyongsu Yi
This paper presents a surround vehicle motion prediction algorithm for multi-lane turn intersections using a Long Short-Term Memory (LSTM)-based Recurrent Neural Network (RNN). The motion predictor is trained using the states of subject and surrounding vehicles, which are collected by sensors mounted on an autonomous vehicle. Data on 484 vehicle trajectories were collected from real traffic situations at multi-lane turn intersections. 11,662 and 4,998 samples acquired from the vehicle trajectories were used to train and evaluate the networks, respectively. A motion planner based on Model Predictive Control (MPC) is designed to determine the longitudinal acceleration command based on the predicted states of surrounding vehicles. The future states of the subject vehicle derived by MPC is used as an input feature to reflect the interaction of subject and target vehicles in LSTM-RNN based motion predictor. The proposed algorithm was evaluated in terms of its accuracy and its effects on the motion planning algorithm based on the driving data sets. The improved prediction accuracy substantially increased safety by bounding the prediction error within the safety margin. The application results of the proposed predictor demonstrate the improved recognition timing of the preceding vehicle and the similarity of longitudinal acceleration with drivers.

30A Predictive Safety Filter for Learning-Based Racing ControlOpenAlex

Ben Tearle, Kim P. Wabersich, Andrea Carron, et al.
The growing need for high-performance controllers in safety-critical applications like autonomous driving motivated the development of formal safety verification techniques. In this letter, we design and implement a predictive safety filter that is able to maintain vehicle safety with respect to track boundaries when paired alongside any potentially unsafe control signal, such as those found in learning-based methods. A model predictive control (MPC) framework is used to create a minimally invasive algorithm that certifies whether a desired control input is safe and can be applied to the vehicle, or that provides an alternate input to keep the vehicle in bounds. To this end, we provide a principled procedure to compute a safe and invariant set for nonlinear dynamic bicycle models using efficient convex approximation techniques. To fully support an aggressive racing performance without conservative safety interventions, the safe set is extended in real-time through predictive control backup trajectories. Applications for assisted manual driving and deep imitation learning on a miniature remote-controlled vehicle demonstrate the safety filter's ability to ensure vehicle safety during aggressive maneuvers.

31Model predictive control of legged and humanoid robots: models and algorithmsOpenAlex

Sotaro Katayama, Masaki Murooka, Yuichi Tazaki
Model predictive control (MPC) of legged and humanoid robotic systems has been an active research topic in the past decade. While MPC for robotic systems has a long history, its paradigm such as problem formulations and algorithms has changed along with the recent drastic progress in robot hardware, computational processors, and algorithms. This survey paper reviews recent progress on MPC for legged and humanoid robotics from the following three points of view. First, we review a variety of dynamical models of robotic systems used in the MPC formulation. Second, we give an overview of MPC algorithms, particularly focusing on suitable ones for robotic problems. Finally, we introduce methods and applications of MPC for practical robotic problems from MPC based on reduced-order models to recent progress on MPC based on whole-body models.

32Adaptive Control for Robotic ManipulatorsOpenAlex

The increasing importance of machine learning in manipulator control is reviewed from two main perspectives: modeling and learning control. The chapter starts with an introduction to history and theory of Model Reference Adaptive Control (MRAC) and its application to manipulator control. Least Square Minimization (LSM) regression is highlighted as the machine learning element in indirect MRAC that seeks to fi nd unknown parameters from a number of data points. The limitations of indirect and direct MRAC are identifi ed. Specifi cally, indirect MRAC is limited by the need for persistent excitation and the use of simple modeling assumptions that lead to undesirable control performance. Direct MRAC is limited by reference model mismatch, adaptation rate, choice of control law, and relying on error feedback correction with the frequent consequence of stability and adaptation problems. Moreover, neither direct nor indirect MRAC can handle state and input constraints which are important in the control of robotic manipulators. Machine learning techniques offer the promise of overcoming these limitations. Recent developments include Concurrent-MRAC which is able to alleviate the persistent excitation requirement for LTI systems and may have application to the control of robotic manipulators. The chapter covers the broader contributions of machine learning to recent developments in manipulator control that combine learning and adaptation. This includes: (i) the use of advanced modeling methods such as Mixture Models and Neural Networks and (ii) learning control methods such as Iterative Learning Control and modern Reinforcement Learning and their relation to adaptive control. State and input constraints are identifi ed to be one of the signifi cant remaining challenges in manipulator control. Model Predictive Control (MPC) is introduced as the control method that can handle state and input constraints in its formulation. A number of recent attempts to incorporate learning capabilities in MPC are discussed.

33Learning Interaction-Aware Trajectory Predictions for Decentralized Multi-Robot Motion Planning in Dynamic EnvironmentsOpenAlex

Hai Zhu, Francisco Martinez Claramunt, Bruno Brito, et al.
This letter presents a data-driven decentralized trajectory optimization approach for multi-robot motion planning in dynamic environments. When navigating in a shared space, each robot needs accurate motion predictions of neighboring robots to achieve predictive collision avoidance. These motion predictions can be obtained among robots by sharing their future planned trajectories with each other via communication. However, such communication may not be available nor reliable in practice. In this letter, we introduce a novel trajectory prediction model based on recurrent neural networks (RNN) that can learn multi-robot motion behaviors from demonstrated trajectories generated using a centralized sequential planner. The learned model can run efficiently online for each robot and provide interaction-aware trajectory predictions of its neighbors based on observations of their history states. We then incorporate the trajectory prediction model into a decentralized model predictive control (MPC) framework for multi-robot collision avoidance. Simulation results show that our decentralized approach can achieve a comparable level of performance to a centralized planner while being communication-free and scalable to a large number of robots. We also validate our approach with a team of quadrotors in real-world experiments.

34Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement LearningOpenAlex

Lukas Brunke, Melissa Greeff, Adam W. Hall, et al.
The last half decade has seen a steep rise in the number of contributions on safe learning methods for real-world robotic deployments from both the control and reinforcement learning communities. This article provides a concise but holistic review of the recent advances made in using machine learning to achieve safe decision-making under uncertainties, with a focus on unifying the language and frameworks used in control theory and reinforcement learning research. It includes learning-based control approaches that safely improve performance by learning the uncertain dynamics, reinforcement learning approaches that encourage safety or robustness, and methods that can formally certify the safety of a learned control policy. As data- and learning-based robot control methods continue to gain traction, researchers must understand when and how to best leverage them in real-world scenarios where safety is imperative, such as when operating in close proximityto humans. We highlight some of the open challenges that will drive the field of robot learning in the coming years, and emphasize the need for realistic physics-based benchmarks to facilitate fair comparisons between control and reinforcement learning approaches.

35Trajectory Tracking Control Algorithm for Autonomous Vehicle Considering Cornering CharacteristicsOpenAlex

Jingwei Cao, Chuanxue Song, Silun Peng, et al.
Trajectory tracking control is a key technology in the research and development of autonomous vehicles. With the aim of addressing problems such as low control accuracy and poor real-time performance, which can occur easily when an autonomous vehicle avoids obstacles, this research focuses on the trajectory tracking control algorithm for autonomous vehicle considering cornering characteristics. First, the vehicle dynamics model and tire model are established through appropriate simplification. Then, based on the basic principle of model predictive control, a linear time-varying model predictive controller (LTV MPC) that considers the cornering characteristics is designed and optimized. Finally, using CarSim and MATLAB/Simulink software, a joint simulation model is established and the trajectory tracking performance of the controlled vehicle under different vehicle speeds and road adhesion conditions are tested through simulation experiments in combination with the double-shift line reference trajectory. The simulation results show the LTV MPC controller that considers cornering characteristics has good self-adaptability under complicated and severe working conditions, and no cases, such as car sideslip or track departure, were observed. Compared with other controllers and algorithms, the designed trajectory tracking controller has remarkable comprehensive performance, exhibits superior robustness and anti-interference ability, and significant improvements in the trajectory tracking control accuracy and real-time performance. The proposed control algorithm is of great importance in improving the tracking stability and driving safety of autonomous vehicles under complex extreme conditions and conducive to the further development and improvement of the technological level of intelligent vehicle driving assistance.

36A practical trajectory tracking control of autonomous vehicles using linear time-varying MPC methodOpenAlex

Hui Pang, Nan Liu, Chuan Hu, et al.
With the rapid development and implementation of autonomous vehicles (AVs), the simultaneous and accurate trajectory tracking problem for such AVs has become a popular research topic. This paper proposes a comprehensive linear time-varying model predictive controller (LTV-MPC) design for a type of AV, aiming to achieve good trajectory tracking in a practical driving scenario. First, a two-degree-of-freedom kinematic model of an AV is established. Next, an error model of the AV’s trajectory tracking system is constructed using linear time-varying theory. A successive linearization is introduced to linearize the nonlinear tracking error model, and a quadratic programming optimization problem is then formulated. Thus, the control sequence for this AV is incorporated into the predictive control framework, and the desired controller can be solved with a relatively higher computational efficiency and lower computational cost. Finally, the effectiveness and performance of the proposed controller are validated via a comparison of simulations conducted using MATLAB software and experiments conducted using a self-established test platform. The results demonstrate that the proposed LTV-MPC method can track the prescribed reference road trajectories with high precision and stability for an AV under various driving conditions.

37Automatic Weight Determination in Model Predictive Control for Personalized Car-Following ControlOpenAlex

Wontaek Lim, Seongjin Lee, Jinsoo Yang, et al.
Car-following control is a fundamental application of autonomous driving. This control has multiple objectives, including tracking a safe distance to a preceding vehicle and enhancing driving comfort. Model Predictive Control (MPC) is a powerful method due to its intuitiveness and capability to cover multiple objectives. MPC determines the relative importance of objectives through a set of weight factors, depending on which, the controller’s behavior changes even if the traffic situations are the same. However, determining the optimal weight is not a trivial problem because there is no benchmark to evaluate the performance of the weight, and searching for weight factors with repeated driving experiments is time-consuming. To solve this problem, we proposed an automatic tuning method to determine the weights of the MPC based on personal driving data. Personal driving data under naturalistic driving conditions provide car-following situations and driver’s behaviors. These data can generate a reference model to represent the driver’s driving style. Based on this model, the proposed method defined the automatic tuning problem as an optimization problem that minimizes the difference between the reference and the controller’s response using the optimal weight factors. This optimization problem was solved using the Particle Swarm Optimization algorithm. The proposed method was implemented with an embedded optimization coder in an offline fashion. Its performance was evaluated using personal driving data. From this, the proposed method can reduce the effort and time required for an engineer to find the optimal weight factors.

38LQR-MPC-Based Trajectory-Tracking Controller of Autonomous Vehicle Subject to Coupling Effects and Driving State UncertaintiesOpenAlex

Tengfei Yuan, Rongchen Zhao
This paper presents a lateral and longitudinal coupling controller for a trajectory-tracking control system. The proposed controller can simultaneously minimize lateral tracking deviation while tracking the desired trajectory and vehicle speed. Firstly, we propose a hierarchical control structure composed of upper and lower-level controllers. In the upper-level controller, the linear quadratic regulator (LQR) controller is designed to compute the desired front wheel steering angle for minimizing the lateral tracking deviation, and the model-predictive controller is developed to compute the desired acceleration for maintaining the planed vehicle speed. The lower-level controller enables the achievement of the desired steering angle and acceleration via the corresponding component devices. Furthermore, an observer based on the Extended Kalman Filter (EKF) is proposed to update the vehicle driving states, which are sensitive to the trajectory-tracking control and difficult to measure directly using the existing vehicle sensors. Finally, the Co-simulation (CarSim-MATLAB/Simulink) results demonstrate that the proposed coupling controller is able to robustly realize the trajectory tracking control and can effectively reduce the lateral tracking error.

39Human-Centered Trajectory Tracking Control for Autonomous Vehicles With Driver Cut-In Behavior PredictionOpenAlex

Yimin Chen, Chuan Hu, Junmin Wang
Trajectory tracking control in the cut-in scenarios is challenging, since the autonomous vehicles have to follow the reference trajectory and cooperate with the cut-in vehicles. This paper proposes a human-centered trajectory tracking control strategy integrating driver behavior prediction for the cut-in scenarios and their transient processes. A recurrent neural network (RNN) with long short-term memory (LSTM) cells is used to predict the driver behaviors of the cut-in vehicle. Then, a model predictive control (MPC) approach considering the driver behaviors of the cut-in vehicle is designed to track the reference trajectory. The transient processes of the cut-in scenarios are considered for different cut-in behaviors. Moreover, the moving horizon estimator (MHE) is used to estimate the vehicle lateral velocity that is used in the controller. Human driver tests on a driving simulator show that the drivers' intention of the cut-in vehicle can be predicted by the RNN with LSTM cells. CarSim <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">®</sup> simulation studies show the human-centered trajectory tracking controller can track the reference trajectory using the estimated vehicle lateral velocity. The autonomous vehicle can cooperate with the cut-in vehicle in different driving situations and obtain smooth transient processes of the cut-in scenarios.

40Combined Trajectory Planning and Tracking for Autonomous Vehicle Considering Driving StylesOpenAlex

Haoran Li, Chaozhong Wu, Duanfeng Chu, et al.
Autonomous driving is one of the promising technologies to tackle traffic accident and congestion problems nowadays. Even though an autonomous vehicle is operated without humans, it is necessary to reflect the driving characteristics of a human driver. This can increase user acceptance to autonomous driving system, which in turn will improve driving safety because of human occupants' trust in it. In this paper, a combined trajectory planning and tracking algorithm is proposed for the vehicle control. Firstly, traffic environments and driving styles are modeled with the Artificial Potential Field (APF) approach. Secondly, those APF values are integrated into the Model Predictive Control (MPC) design process, which can optimize the trajectories and control outputs. In this way, we add people's driving habits and styles into the controller, so that the controlled vehicle can move under the effects of the traffic environments and human's driving styles. At last, autonomous driving, which reflects two types of human drivers' driving styles (a cautious driving style and an aggressive one), is tested by the simulation experiments in two scenarios (car-following and lane-changing). Furthermore, the result demonstrates that the proposed algorithm can reflect driving styles. Accordingly, this novel controller can be utilized in the autonomous vehicle control field.

41An Introduction to Deep Reinforcement LearningOpenAlex

Vincent François-Lavet, Peter Henderson, Riashat Islam, et al.
Deep reinforcement learning is the combination of reinforcement learning (RL) and deep learning. This field of research has been able to solve a wide range of complex decision making tasks that were previously out of reach for a machine. Thus, deep RL opens up many new applications in domains such as healthcare, robotics, smart grids, finance, and many more. This manuscript provides an introduction to deep reinforcement learning models, algorithms and techniques. Particular focus is on the aspects related to generalization and how deep RL can be used for practical applications. We assume the reader is familiar with basic machine learning concepts.

42Lane-Changing Tracking Control of Automated Vehicle Platoon Based on MA-DDPG and Adaptive MPCOpenAlex

Jintao Wan, Hongfei Liu, Miao Xu, et al.
To address the problem of autonomous lane-changing maneuvers for automated vehicle platoons on highways, a novel platoon lane-changing (PLC) tracking control framework based on the multi-agent Deep Deterministic Policy Gradient (MA-DDPG) and adaptive model predictive control (AMPC) is presented. Currently, the classic platoon cooperative control method is complex in structure and necessitates the establishment of an accurate vehicle dynamics model, so a fully decentralized MA-DDPG algorithm is proposed to realize the longitudinal following control, handling nonlinear systems and continuous state space. The agents associated with each following vehicle stay in communication via the predecessor-leader following (PLF) or predecessor following (PF) communication topology, training locally. Secondly, the traditional MPC is prone to large fluctuations in the early stage of solving and its tracking performance deteriorates with varied longitudinal speed. Therefore, an AMPC controller whose prediction time domain changes with the longitudinal speed is combined with the quintic polynomial curve to complete the lateral control, and a fuzzy controller is introduced for compensation of front wheel steering angles. The results of the joint Carsim/Simulink simulation demonstrate that the AMPC controller can achieve lateral tracking control under working conditions of 50 km/h, 100 km/h, and variable speed, and the front wheel steering angles are also stable. The MA-DDPG algorithm can achieve effective following control when the longitudinal expected speed is 25 m/s. The framework proposed in this study can both track effectively and smooth the longitudinal velocity profile compared with algorithm combinations 1: CACC with AMPC and 2: CACC with PID.

43Cooperative Path Following of Autonomous Vehicles with Model Predictive Control and Event Triggered CommunicationsOpenAlex

Nguyen T. Hung, A. Pascoal
This paper presents a solution to the problem of multiple vehicle cooperative path following (CPF) that takes explicitly into account the constraints on the vehicles inputs and the topology of the inter-vehicle communications network. The solution involves decoupling the original constrained CPF problem into two sub-problems: i) single vehicle constrained path following and ii) multi-agent system (MAS) coordination. The first is solved by adopting a sampled-data model predictive control (MPC) scheme, whereas the latter is tackled by using a distributed control law with an event triggered communication (ETC) mechanism. We show that this design methodology yields a stable closed-loop CPF system: the path following error for each vehicle is globally asymptotically stable (GAS) and the coordination errors between the vehicles are bounded. A simulation example consisting of three autonomous vehicles following a given 2D- desired formation illustrates the efficacy of the CPF strategy proposed.

44Planning and Decision-Making for Autonomous VehiclesOpenAlex

Wilko Schwarting, Javier Alonso–Mora, Daniela Rus
In this review, we provide an overview of emerging trends and challenges in the field of intelligent and autonomous, or self-driving, vehicles. Recent advances in the field of perception, planning, and decision-making for autonomous vehicles have led to great improvements in functional capabilities, with several prototypes already driving on our roads and streets. Yet challenges remain regarding guaranteed performance and safety under all driving circumstances. For instance, planning methods that provide safe and system-compliant performance in complex, cluttered environments while modeling the uncertain interaction with other traffic participants are required. Furthermore, new paradigms, such as interactive planning and end-to-end learning, open up questions regarding safety and reliability that need to be addressed. In this survey, we emphasize recent approaches for integrated perception and planning and for behavior-aware planning, many of which rely on machine learning. This raises the question of verification and safety, which we also touch upon. Finally, we discuss the state of the art and remaining challenges for managing fleets of autonomous vehicles.

45Cost-Optimal Energy Management of Hybrid Electric Vehicles Using Fuel Cell/Battery Health-Aware Predictive ControlOpenAlex

Xiaosong Hu, Changfu Zou, Xiaolin Tang, et al.
Energy management is an enabling technology for increasing the economy of fuel cell/battery hybrid electric vehicles. Existing efforts mostly focus on optimization of a certain control objective (e.g., hydrogen consumption), without sufficiently considering the implications for on-board power sources degradation. To address this deficiency, this article proposes a cost-optimal, predictive energy management strategy, with an explicit consciousness of degradation of both fuel cell and battery systems. Specifically, we contribute two main points to the relevant literature, with the purpose of distinguishing our study from existing ones. First, a model predictive control framework, for the first time, is established to minimize the total running cost of a fuel cell/battery hybrid electric bus, inclusive of hydrogen cost and costs caused by fuel cell and battery degradation. The efficacy of this framework is evaluated, accounting for various sizes of prediction horizon and prediction uncertainties. Second, the effects of driving and pricing scenarios on the optimized vehicular economy are explored.

46MPC Control and Path Planning of Omni-Directional Mobile Robot with Potential Field MethodOpenAlex

Xiaofeng Liu, Hailin Chen, Chengcheng Wang, et al.

47Nonholonomic mobile robots' trajectory tracking model predictive control: a surveyOpenAlex

Tiago Nascimento, Carlos E.T. Dórea, Luiz Marcos Garcia Gonçalves
SUMMARY Model predictive control (MPC) theory has gained attention with the recent increase in the processing power of computers that are now able to perform the needed calculations for this technique. This kind of control algorithms can achieve better results in trajectory tracking control of mobile robots than classical control approaches. In this paper, we present a review of recent developments in trajectory tracking control of mobile robot systems using model predictive control theory, especially when nonholonomicity is present. Furthermore, we point out the growth of the related research starting with the boom of mobile robotics in the 90s and discuss reported field applications of the described control problem. The objective of this paper is to provide a unified and accessible presentation, placing the classical model, problem formulations and approaches into a proper context and to become a starting point for researchers who are initiating their endeavors in linear/nonlinear MPC applied to nonholonomic mobile robots. Finally, this work aims to present a comprehensive review of the recent breakthroughs in the field, providing links to the most interesting and successful works, including our contributions to state-of-the-art.

48MPC-based high-speed trajectory tracking for 4WIS robotOpenAlex

Xinxin Liu, Wei Wang, Xuelong Li, et al.

49MPC Based Path Planning for Wheeled Mobile Robots in Environments with Varying SlipOpenAlex

Harinarayanan Nampoothiri M G, Rahul Antony
The paper aims to address the challenges involved in the control design of Wheeled Mobile Robots (WMR) under the conditions of slip. The work is done as part of investigating the possibilities of using advancements in Machine Learning techniques in WMR with the integration of modern control strategies. The research presents a dynamic model of the robot including four slip parameters and wheel torques as input. The navigation in different environments can be affected by these slip variables resulting from disturbances including terrain dynamics. A model predictive control (MPC) is used to manipulate the torque variables according to the path and variation in both longitudinal and lateral slip values. By proposing the torque control, the work can be extended to Ground Robots with different payloads. The model can follow the reference path with linear and angular velocity constraints. It is also identified that the proposed MPC can adapt to the slip variations which are observed from the change in linear velocities and accelerations under different test values of slip variables. The slip parameters can be identified in real-time with the help of machine learning techniques and can provide a reference to the MPC model proposed. In the future, Artificial Intelligence (AI) can be integrated with control system design to address the multi-terrain navigation challenges.

50Model predictive control for the tracking of autonomous mobile robot combined with a local path planningOpenAlex

Jianhua Li, Jianfeng Sun, Liqun Liu, et al.
This article presents a model predictive control (MPC) coupled with an artificial potential field (APF) to resolve the trajectory tracking while considering the obstacle avoidance. In this article, the obstacle avoidance problem is solved by a local path planning based on the artificial potential field by constructing a virtual goal. A virtual goal is generated to produce an attractive force to guide the mobile robot to a collision-free space. The planned path is controlled by a proportional–integral–derivative (PID) controller to avoid collision. After arriving at the virtual goal, an off-line explicit MPC is calculated to obtain the optimal control inputs to track the reference trajectory. The simulation results show that the proposed method can be applied to control the mobile robot in the environment with one obstacle.

51Autonomous Navigation of Magnetic Microrobots in a Large Workspace Using Mobile-Coil SystemOpenAlex

Zhengxin Yang, Lidong Yang, Li Zhang
Untethered magnetic miniature robots have attracted much attention in recent years, due to their minimally invasive features in biomedicine and highly flexible traits in micromanipulation. Autonomous control is one of the essential issues for magnetic microrobots, however, which remains challenging, especially for complex and large-workspace environments. To this end, this article proposes a novel navigation framework, using a home-designed eye-in-hand mobile-coil system. A three-step motion planner is designed to know entire surroundings and generate optimal paths, which contains environment reconstruction, position registration, and modified A* path searching. Moreover, a double-loop motion controller is designed to make the microrobot accurately follow the computed path and intelligently avoid collisions: The inner loop performs mechanism following; the outer loop decides appropriate magnetic fields for actuation, which includes a disturbance observer (DOB), a fuzzy logic modifier (FLM), and a model predictive controller (MPC). Experiments demonstrate the effectiveness of the proposed strategy: Feasible trajectories in a maze-like environment of diameter 230 mm can be planned, and autonomous navigation of microrobot is realized with both global accessibility and local adaptability.

52Decentralized Multi-Robot Collision Avoidance: A Systematic Review from 2015 to 2021OpenAlex

Mehak Raibail, Abdul Hadi Abd Rahman, Ghassan Jasim AL-Anizy, et al.
An exploration task can be performed by a team of mobile robots more efficiently than human counterparts. They can access and give live updates for hard-to-reach areas such as a disaster site or a sewer. However, they face some issues hindering them from optimal path planning due to the symmetrical shape of the environments. Multiple robots are expected to explore more areas in less time while solving robot localization and collision-avoidance issues. When deploying a multi-robot system, it is ensured that the hardware parts do not collide with each other or the surroundings, especially in symmetric environments. Two types of methods are used for collision avoidance: centralized and decentralized. The decentralized approach has mainly been used in recent times, as it is computationally less expensive. This article aims to conduct a systematic literature review of different collision-avoidance strategies and analyze the performance of innovative collision-avoidance techniques. Different methods such as Reinforcement Learning (RL), Model Predictive Control (MPC), Altruistic Coordination, and other approaches followed by selected studies are also discussed. A total of 17 studies are included in this review, extracted from seven databases. Two experimental designs are studied: empty/open space and confined indoor space. Our analysis observed that most of the studies focused on empty/open space scenarios and verified the proposed model only through simulation. ORCA is the primary method, against which all the state-of-the-art techniques are evaluated. This article provides a comparison between different methods used for multi-robot collision avoidance. It discusses if the methods used are focused on safety or path planning. It also sheds light on the limitations of the studies included and possible future directions.

53Interaction Force Constraints for Position-Controlled Manipulator Using Linear MPCOpenAlex

Nicola Piccinelli, Riccardo Muradore
The control of the interaction force between the environment and the manipulator in safety-critical scenarios, like surgery, search-and-rescue or industrial plant maintenance, can prevent damage or unwanted behaviour. If the manipulator software provides only position-based or velocity-based control loops, controlling the interaction forces is a challenging problem. For this reason, Model Predictive Control (MPC) has started to be adopted also in the field of real-time force control thanks to its capability of integrating constraints. In this paper, we propose a linear model predictive force control able to guarantee safe interaction with an unknown environment by constraining the interaction force. The environment is modelled together with the robot dynamics and, thanks to the estimation of the low-level controller, the proposed methodology can be applied to any robotic manipulator without a direct joint torque control loop. The MPC controller with force constraint has been validated in a real scenario using a UR5e collaborative robot in a polishing-like task.

54Position Control and Force Allocation Algorithms for HybridPneumatic-Electric Linear ActuatorsOpenAlex

Behrad Rouzbeh, Gary M. Bone
It has been shown that hybrid pneumatic electric actuators (HPEAs) can provide both accurate position control and high inherent safety, due to their low mechanical impedance; making them a suitable choice to be used in applications such as collaborative robots. HPEAs are redundant actuators that combine the large force, low bandwidth characteristics of pneumatic actuators with the large bandwidth, small force characteristics of electric actuators. If these characteristics are mathematically modelled, input allocation techniques can improve the HPEA performance by intelligently distributing the required input (force or torque) between the redundant actuators. In this study, after developing a model for a HPEA-driven system, a model-predictive control (MPC) approach is designed that employ this model and solve the position tracking and input allocation problem using convex optimization. Another approach based on conventional linear controllers is included and compared. Although the linear controller was more computationally-efficient, it was inferior to the MPC-based controller in position tracking and force allocation performance. The MPC-based controller with a two-layer structure reduced the position RMSE by 59%, the mean absolute electric actuator force by 36%, and the mean absolute pneumatic actuator force by 24% relative to the linear controller. It can also be computed fast enough for real-time operation.

55Advances in Control Techniques for Rehabilitation Exoskeleton Robots: A Systematic ReviewOpenAlex

Gazi Abdullah Mashud, Sk Hasan, Nafizul Alam
This systematic review explores recent advancements in control methods for rehabilitation exoskeleton robots, which assist individuals with motor impairments through guided movement. As robotics technology progresses, precise, adaptable, and safe control techniques have become accessible for effective human–robot interaction in rehabilitation settings. Key control methods, including computed torque and adaptive control, excel in managing complex movements and adapting to diverse patient needs. Robust and sliding mode controls address stability under unpredictable conditions. Traditional approaches, like PD and PID control schemes, maintain stability, performance, and simplicity. In contrast, admittance control enhances user–robot interaction by balancing force and motion. Advanced methods, such as model predictive control (MPC) and Linear Quadratic Regulator (LQR), provide optimization-based solutions. Intelligent controls using neural networks, Deep Learning, and reinforcement learning offer adaptive, patient-specific solutions by learning over time. This review provides an in-depth analysis of these control strategies by examining advancements in recent scientific literature, highlighting their potential to improve rehabilitation exoskeletons, and offering future recommendations for greater efficiency, responsiveness, and patient-centered functionality.

56BiConMP: A Nonlinear Model Predictive Control Framework for Whole Body Motion PlanningOpenAlex

Avadesh Meduri, Paarth Shah, Julian Viereck, et al.
Online planning of whole-body motions for legged robots is challenging due to the inherent nonlinearity in the robot dynamics. In this work, we propose a nonlinear model predictive control (MPC) framework, the BiConMP which can generate whole body trajectories online by efficiently exploiting the structure of the robot dynamics. BiConMP is used to generate various cyclic gaits on a real quadruped robot and its performance is evaluated on different terrain, countering unforeseen pushes, and transitioning online between different gaits. Furthermore, the ability of BiConMP to generate nontrivial acyclic whole-body dynamic motions on the robot is presented. The same approach is also used to generate various dynamic motions in MPC on a humanoid robot (Talos) and another quadruped robot (AnYmal) in simulation. Finally, an extensive empirical analysis on the effects of planning horizon and frequency on the nonlinear MPC framework is reported and discussed.

57Full-Body Optimal Control Toward Versatile and Agile Behaviors in a Humanoid RobotOpenAlex

Koji Ishihara, Takeshi Itoh, Jun Morimoto
In this letter, we develop an optimal control framework that takes the full-body dynamics of a humanoid robot into account. Employing full-body dynamics has been explored in, especially, an online optimal control approach known as model predictive control (MPC). However, whole-body motions cannot be updated in a short period of time due to MPC's large computational burden. Thus, MPC has generally been evaluated with a physical humanoid robot in a limited range of tasks where high-speed motion executions are unnecessary. To cope with this problem, our multi-timescale control framework drives whole-body motions with a computationally efficient hierarchical MPC. Meanwhile, a biologically inspired controller maintains the robot's posture for a very short control period. We evaluated our framework in skating tasks with simulated and real lower-body humanoids that have rollers on the feet. Our simulated robot generated various agile motions such as jumping over a bump and flipping down from a cliff in real time. Our real lower-body humanoid also successfully generated a movement down a slope.

58First Order Approximation of Model Predictive Control Solutions for High Frequency FeedbackOpenAlex

Ewen Dantec, Michel Taïx, Nicolas Mansard
The lack of computational power on mobile robots is a well-known challenge when it comes to implementing a real-time MPC scheme to perform complex motions. Currently the best solvers are barely able to reach 100 Hz for computing the control of a whole-body legged model, while modern robots are expecting new torque references in less than 1 ms. This problem is usually tackled by using a handcrafted low-level tracking control whose inputs are the low-frequency trajectory computed by the MPC. We show that a linear state feedback controller naturally arises from the optimal control formulation and can be used directly in the low-level control loop along with other sensitivities of relevant time-varying parameters of the problem. When the optimal control problem is solved by DDP, this linear controller can be computed for cheap as a by-product of the backward pass, and corresponds in part to the classical Riccati gains. A side effect of our proposition is to show that Riccati gains are valuable assets that must be used to achieve an efficient control and that they are not stiffer than the optimal control scheme itself. We propose a complete implementation of this idea on a full-scale humanoid robot and demonstrate its importance with real experiments on the robot Talos.

59A Whole-Body Model Predictive Control Scheme Including External Contact Forces and CoM Height VariationsOpenAlex

Reihaneh Mirjalili, Aghil Yousefi-Korna, Farzad A. Shirazi, et al.
In this paper, we present an approach for generating a variety of whole-body motions for a humanoid robot. We extend the available Model Predictive Control (MPC) approaches for walking on flat terrain to plan for both vertical motion of the Center of Mass (CoM) and external contact forces consistent with a given task. The optimization problem is comprised of three stages, i. e. the CoM vertical motion, joint angles and contact forces planning. The choice of external contact (e. g. hand contact with the object or environment) among all available locations and the appropriate time to reach and maintain a contact are all computed automatically within the algorithm. The presented algorithm benefits from the simplicity of the Linear Inverted Pendulum Model (LIPM), while it overcomes the common limitations of this model and enables us to generate a variety of whole body motions through external contacts. Simulation and experimental implementation of several whole body actions in multi-contact scenarios on a humanoid robot show the capability of the proposed algorithm.

60Online Adaptive Motion Generation for Humanoid Locomotion on Non-Flat Terrain via Template Behavior ExtensionOpenAlex

Xiang Meng, Zhangguo Yu, Xuechao Chen, et al.
For humanoid robots, online motion generation on non-flat terrain remains an ongoing research challenge. Computational complexity is one of the primary restrictions that preclude motion planners from generating adaptive behaviors online. In this paper, we investigate this problem and decompose it into two sequential components: an Efficient Behavior Generator (EBG) and a Nonlinear Centroidal Model Predictive Controller (NC-MPC). The EBG is responsible for optimizing the physically feasible whole-body template behaviors, which can provide reliable warm-starts for NC-MPC, thereby greatly reducing the computational effort of online planning. With tailored objective function and feet complementary constraints, the EBG can search for a near-optimal solution after several iterations within seconds for different behaviors including walking, running, and jumping, even with intuitive initial guesses. To make the template behaviors extensible when the robot encounters possible different scenarios, the NC-MPC is proposed to regenerate the reactive motion online to adapt it to the real local environment. Finally, we validate the effectiveness of synthesizing EBG and NC-MPC for humanoid locomotion on non-flat terrain in simulation and on the real humanoid robot BHR7P. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> — For current humanoid robots, dynamically traversing non-flat terrain such as stairs, slopes, and gaps in the real world presents a significant challenge. In this paper, we propose an adaptive motion planner for humanoid robots to traverse non-flat terrain, which is properly integrated into the closed loop of online control. Considering computational complexity and motion extensibility, the planner consists of two parts: an efficient behavior generator performed offline and a nonlinear model predictive controller performed online. The behavior generator can efficiently generate template behaviors for the humanoid robot, including various gaits such as walking, running, and jumping. To make these template behaviors adaptable, a nonlinear model predictive controller based on the centroidal dynamics model is developed to plan reactive motions online. It can extend template behaviors to fit potentially different scenarios in practice. The proposed method is validated in simulations and experiments with the humanoid robot BHR7P. Furthermore, this method can be applied to legged robots or systems that need to move dynamically on non-flat terrain, such as quadruped and hexapod robots.

61Model predictive control: Theory and practice—A surveyOpenAlex

Carlos E. García, David M. Prett, Manfred Morari

62Model predictive control: Theory and practiceOpenAlex

Manfred Morari, Carlos E. García, David M. Prett

63Next generation controllers for kiln/cooler and mill applications based on model predictive control and neural networksOpenAlex

Greg Martin, T. Lange, N. Frewin
Model predictive control (MPC) has become the standard supervisory control tool in some process industries, including oil refining and petrochemicals. It has been introduced into the cement industry, in a kiln/cooler application at Pretoria Portland Cement's (PPC) Dwaalboom plant in South Africa. This application differs from the well-established expert system approach in that it incorporates a model of the process rather than a model of the operator. The continuous regulation and disturbance rejection of MPC is well suited to kiln/cooler control, and for example the application recovers from major upsets such as coating drop three times faster than typical operator intervention. Mills have been known to demonstrate severe nonlinear behavior, and linear controllers in mill applications have yielded only varying degrees of success. Most applications are eventually turned off due to poor performance caused by this nonlinear behaviour. Nonlinear MPC has been applied to the cement mill at Dwaalboom-a closed circuit ball mill. Gains are calculated at each control execution using a neural network model built from three months of log sheet data. Gains in the controller change by as much as a factor of fifteen. This controller has demonstrated significantly improved setpoint tracking and disturbance rejection over all three-product grades.

64Model predictive control strategy for petrochemical supply chain planning under uncertaintyOpenAlex

Jishuai Wang
This paper applies model predictive control (MPC), which is an advanced control technique to supply chain planning arising in petrochemical industry. A multi-period, multi-product planning under uncertainty is discussed. The usefulness of MPC as a tactical decision policy is integrated to the model. Based on the discrete-time modeling method, a mixed integer linear programming (MILP) model is introduced, in which the nonlinear part is converted to linear problem using fuzzy possibility method. The effectiveness of the proposed model is illustrated through a refinery case.

65Model Predictive Control for Distributed Microgrid Battery Energy Storage SystemsOpenAlex

Thomas Morstyn, Branislav Hredzak, Ricardo P. Aguilera, et al.
This brief proposes a new convex model predictive control (MPC) strategy for dynamic optimal power flow between battery energy storage (ES) systems distributed in an ac microgrid. The proposed control strategy uses a new problem formulation, based on a linear d-q reference frame voltage-current model and linearized power flow approximations. This allows the optimal power flows to be solved as a convex optimization problem, for which fast and robust solvers exist. The proposed method does not assume that real and reactive power flows are decoupled, allowing line losses, voltage constraints, and converter current constraints to be addressed. In addition, nonlinear variations in the charge and discharge efficiencies of lithium ion batteries are analyzed and included in the control strategy. Real-time digital simulations were carried out for an islanded microgrid based on the IEEE 13 bus prototypical feeder, with distributed battery ES systems and intermittent photovoltaic generation. It is shown that the proposed control strategy approaches the performance of a strategy based on nonconvex optimization, while reducing the required computation time by a factor of 1000, making it suitable for a real-time MPC implementation.

66A Centralized Energy Management System for Isolated MicrogridsOpenAlex

Daniel Olivares, Claudio A. Cañizares, Mehrdad Kazerani
This paper presents the mathematical formulation of the microgrid's energy management problem and its implementation in a centralized Energy Management System (EMS) for isolated microgrids. Using the model predictive control technique, the optimal operation of the microgrid is determined using an extended horizon of evaluation and recourse, which allows a proper dispatch of the energy storage units. The energy management problem is decomposed into Unit Commitment (UC) and Optimal Power Flow (OPF) problems in order to avoid a mixed-integer non-linear formulation. The microgrid is modeled as a three-phase unbalanced system with presence of both dispatchable and non-dispatchable distributed generation. The proposed EMS is tested in an isolated microgrid based on a CIGRE medium-voltage benchmark system. Results justify the need for detailed three-phase models of the microgrid in order to properly account for voltage limits and procure reactive power support.

67Model Predictive Control of Distributed Air-Conditioning Loads to Compensate Fluctuations in Solar PowerOpenAlex

Nariman Mahdavi, Julio H. Braslavsky, María M. Serón, et al.
Flexible loads such as residential air-conditioners (ACs) can be directly controlled to provide demand-side regulation and balance services in electricity grids. Large aggregations of ACs offer a resource akin to that of a distributed energy storage system, which may be used to compensate fluctuations in the power output of local renewable energy generation. This paper formulates distributed and centralized model predictive control (MPC) strategies to balance fluctuations in solar power generation by directly controlling the aggregate demand of clusters of distributed residential ACs. The proposed receding-horizon control strategies rely on a new second-order linear time-varying model for the aggregate demand response of a population of heterogeneous ACs to changes in thermostat setpoints under varying ambient temperature. The performance of the proposed MPC strategies is analyzed in a numerical simulation study implementing AC demand tracking of 1-min fluctuations in actual photovoltaic capacity based on persistence and sky imager short-term solar forecasts. The results show that distributed and centralized MPC strategies achieve comparable performance, with better performance of persistence forecasts in a shorter prediction horizon, and better performance with sky imager forecasts on a longer prediction horizon.

68Identification of models for control of wet granulationOpenAlex

Constantijn Sanders, Michael J. Hounslow, Francis J. Doyle

69MPC Relevant Identification Method for Hammerstein ModelsOpenAlex

Raphael Quachio, Claudio García
MPC Controllers are widely applied in the process industry, notably in Oil Refining and Petrochemical processes. MPC Relevant Identification (MRI) methods have been developed to identify models suitable for linear MPC controllers. However, most chemical processes exhibit nonlinear dynamics, for which linear MPC controllers are suitable only for a limited operating range. This paper presents an MRI method for obtaining nonlinear models with polynomial Hammerstein structure. The algorithm is applied in the identification of data from an electric heater. The obtained results indicate that the proposed method generated satisfactory results.

70Nonlinear model predictive control using neural networksOpenAlex

S. Piche, B. Sayyarrodsari, Doug Johnson, et al.
A neural-network-based technique for developing nonlinear dynamic models from empirical data for an model predictive control (MPC) algorithm is presented. These models can be derived for a wide variety of processes and can also be used efficiently in an MPC framework. The nonlinear MPC-based approach presented has been successfully implemented in a number of industrial applications in the refining, petrochemical, pulp and paper, power, and food industries. Performance of the controller on a nonlinear industrial process, a polyethylene reactor, and a simulated continuous stirred tank reactor is presented.

71Machine learning‐based predictive control of nonlinear processes. Part I: TheoryOpenAlex

Zhe Wu, Anh Tran, David Rincón, et al.
Abstract This article focuses on the design of model predictive control (MPC) systems for nonlinear processes that utilize an ensemble of recurrent neural network (RNN) models to predict nonlinear dynamics. Specifically, RNN models are initially developed based on a data set generated from extensive open‐loop simulations within a desired process operation region to capture process dynamics with a sufficiently small modeling error between the RNN model and the actual nonlinear process model. Subsequently, Lyapunov‐based MPC (LMPC) that utilizes RNN models as the prediction model is developed to achieve closed‐loop state boundedness and convergence to the origin. Additionally, machine learning ensemble regression modeling tools are employed in the formulation of LMPC to improve prediction accuracy of RNN models and overall closed‐loop performance while parallel computing is utilized to reduce computation time. Computational implementation of the method and application to a chemical reactor example is discussed in the second article of this series.

72Real-Time Optimization and Control of Nonlinear Processes Using Machine LearningOpenAlex

Zhihao Zhang, Zhe Wu, David Rincón, et al.
Machine learning has attracted extensive interest in the process engineering field, due to the capability of modeling complex nonlinear process behavior. This work presents a method for combining neural network models with first-principles models in real-time optimization (RTO) and model predictive control (MPC) and demonstrates the application to two chemical process examples. First, the proposed methodology that integrates a neural network model and a first-principles model in the optimization problems of RTO and MPC is discussed. Then, two chemical process examples are presented. In the first example, a continuous stirred tank reactor (CSTR) with a reversible exothermic reaction is studied. A feed-forward neural network model is used to approximate the nonlinear reaction rate and is combined with a first-principles model in RTO and MPC. An RTO is designed to find the optimal reactor operating condition balancing energy cost and reactant conversion, and an MPC is designed to drive the process to the optimal operating condition. A variation in energy price is introduced to demonstrate that the developed RTO scheme is able to minimize operation cost and yields a closed-loop performance that is very close to the one attained by RTO/MPC using the first-principles model. In the second example, a distillation column is used to demonstrate an industrial application of the use of machine learning to model nonlinearities in RTO. A feed-forward neural network is first built to obtain the phase equilibrium properties and then combined with a first-principles model in RTO, which is designed to maximize the operation profit and calculate optimal set-points for the controllers. A variation in feed concentration is introduced to demonstrate that the developed RTO scheme can increase operation profit for all considered conditions.

73Nonlinear Predictive Control Using Neural Nets-Based Local Linearization ARX Model—Stability and Industrial ApplicationOpenAlex

Hui Peng, Kazushi Nakano, H. Shioya
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A Gaussian radial basis function (RBF) neural networks-based local linearization autoregressive with exogenous (ARX) model is utilized for describing the dynamics of a class of smooth nonlinear and nonstationary industrial processes. The dynamics of the underlying processes may be treated as the system operating-point-dependent time-varying locally-linear behavior. The RBF-ARX model is a pseudo-linear ARX model identified offline, and its functional coefficients are composed of the operating-point-dependent RBF neural networks. The RBF-ARX model-based predictive control (MPC) design to the nonlinear process is presented, and stability analysis of the nonlinear MPC under some conditions is discussed. Especially, the feasibility and effectiveness as well as the significant performance improvements of the nonlinear MPC design proposed is demonstrated with a real industrial application to the nitrogen oxide (NO$_{\rm x}$) decomposition (de-NO$_{\rm x}$) process in thermal power plants. </para>

74Economic model predictive control of nonlinear process systems using Lyapunov techniquesOpenAlex

Mohsen Heidarinejad, Jinfeng Liu, Panagiotis D. Christofides
Abstract In this work, we develop model predictive control (MPC) designs, which are capable of optimizing closed‐loop performance with respect to general economic considerations for a broad class of nonlinear process systems. Specifically, in the proposed designs, the economic MPC optimizes a cost function, which is related directly to desired economic considerations and is not necessarily dependent on a steady‐state—unlike conventional MPC designs. First, we consider nonlinear systems with synchronous measurement sampling and uncertain variables. The proposed economic MPC is designed via Lyapunov‐based techniques and has two different operation modes. The first operation mode corresponds to the period in which the cost function should be optimized (e.g., normal production period); and in this operation mode, the MPC maintains the closed‐loop system state within a predefined stability region and optimizes the cost function to its maximum extent. The second operation mode corresponds to operation in which the system is driven by the economic MPC to an appropriate steady‐state. In this operation mode, suitable Lyapunov‐based constraints are incorporated in the economic MPC design to guarantee that the closed‐loop system state is always bounded in the predefined stability region and is ultimately bounded in a small region containing the origin. Subsequently, we extend the results to nonlinear systems subject to asynchronous and delayed measurements and uncertain variables. Under the assumptions that there exist an upper bound on the interval between two consecutive asynchronous measurements and an upper bound on the maximum measurement delay, an economic MPC design which takes explicitly into account asynchronous and delayed measurements and enforces closed‐loop stability is proposed. All the proposed economic MPC designs are illustrated through a chemical process example and their performance and robustness are evaluated through simulations. © 2011 American Institute of Chemical Engineers AIChE J, 2012

75Economic Nonlinear Model Predictive ControlOpenAlex

Timm Faulwasser, Lars Grüne, Matthias A. Müller
Model Predictive Control (MPC) can be dated back to the 1960s, and can now be regarded as a mature control method, which has had significant impact on industrial process control. It is applied in many control systems and has been extended to include non-linear dynamics and non-convex constraints. Of increasing importance in all such control systems in the economic benefits within the design of the system. Traditionally, the so-called control pyramid has been the main technique to do this, whereby economic targets are translated into setpoints and reference trajectories, which are in turn stabilized by control techniques such as MPC. At the same time, in process systems engineering and other fields of application, one aims at economic process operation and much attention has been given to this and the term Economic Model Predictive Control (EMPC) has been coined. Economic Nonlinear Model Predictive Control provides a concise overview of different approaches on the question of stability and optimality in different formulations of EMPC. It is the first monograph to cover approaches both with and without terminal constraints and end penalties, and turnpike/dissipativity-based settings as well as Lyapunov-based approaches. This monograph is an accessible tutorial on the state-of-the-art in model predictive control. Students and researchers will find a clear exposition of current knowledge upon which they can build their own research.

76do-mpc: Towards FAIR nonlinear and robust model predictive controlOpenAlex

Felix Fiedler, Benjamin Karg, Lukas Lüken, et al.
Over the last decades, model predictive control (MPC) has shown outstanding performance for control tasks from various domains. This performance has further improved in recent years with advanced MPC schemes for nonlinear systems under uncertainty including economic control objectives. These recent improvements often fail to bridge the gap between MPC researchers and control practitioners in academia and industry, where classical control approaches and traditional linear MPC still dominate most applications. This is despite the fact that advanced MPC controllers can lead to significant energy savings, yield improvements, safer operation and other benefits. In this work, we identify four main obstacles hindering the widespread adoption of advanced MPC methods. These are the unavailability of models, the challenges associated with deploying complex controllers on physical systems, the scarcity of rapid prototyping tools for advanced methods and the limited reproducibility and reusability of advanced MPC controllers and their results. We find that the FAIR principles (findable, accessible, interoperable, reusable) for scientific data-management and research software can play an important role in tackling these obstacles. Following these guidelines, we discuss FAIR solutions and present the open-source software do-mpc as a concrete implementation. The presented solutions include interoperability with neural network toolboxes to simplify nonlinear system identification, interoperability with the OPC UA communication protocol for deployment, and a reproducible data-sampling framework for transparent controller validation, system identification and approximate MPC. The potential of the proposed solutions is illustrated with several simulation studies.

77A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical SystemsOpenAlex

Derui Ding, Qing‐Long Han, Zidong Wang, et al.
Industrial cyber-physical systems (CPSs) are large-scale, geographically dispersed, and life-critical systems, in which lots of sensors and actuators are embedded and networked together to facilitate real-time monitoring and closed-loop control. Their intrinsic features in geographic space and resources put forward to urgent requirements of reliability and scalability for designed filtering or control schemes. This paper presents a review of the state-of-the-art of distributed filtering and control of industrial CPSs described by differential dynamics models. Special attention is paid to sensor networks, manipulators, and power systems. For real-time monitoring, some typical Kalman-based distributed algorithms are summarized and their performances on calculation burden and communication burden, as well as scalability, are discussed in depth. Then, the characteristics of non-Kalman cases are further disclosed in light of constructed filter structures. Furthermore, the latest development is surveyed for distributed cooperative control of mobile manipulators and distributed model predictive control in industrial automation systems. By resorting to droop characteristics, representative distributed control strategies classified by controller structures are systematically summarized for power systems with the requirements of power sharing and voltage and frequency regulation. In addition, distributed security control of industrial CPSs is reviewed when cyber-attacks are taken into consideration. Finally, some challenges are raised to guide the future research.

78Networked distributed model predictive control for multi-variable coupling processOpenAlex

Aimin An, Kejian Han, Lu Zhu, et al.
Networked Distributed Model Predictive Control (NDMPC) is an effective control strategy which is usually used to control large-scale industrial processes with multi-variable coupling. However, data transmission and information exchange are carried out through the network in this control system, it will inevitably appear the phenomenon of network time-varying delay and data packet dropout, which will lead to the overall performance and stability of the system. How to design a networked controller that can satisfy the optimization control of the subsystem and meet the constraint conditions are the key. In this paper, combined with the networked model predictive control strategy with a comparison process based on coordination, to compensate for time-varying delays in communication between subsystems. As a study case, an overall integrated plant which composes of two-unit connected via other processes and intermediate tanks under severe constraints is used to demonstrate the effectiveness and usability of this framework.

79Iterative Distributed Model Predictive Control of Nonlinear Systems: Handling Asynchronous, Delayed MeasurementsOpenAlex

Jinfeng Liu, Xianzhong Chen, David Muñoz de la Peña, et al.
In this work, we focus on iterative distributed model predictive control (DMPC) of large-scale nonlinear systems subject to asynchronous, delayed state feedback. The motivation for studying this control problem is the presence of asynchronous, delayed measurement samplings in chemical processes and the potential use of networked sensors and actuators in industrial process control applications to improve closed-loop performance. Under the assumption that there exist upper bounds on the time interval between two successive state measurements and on the maximum measurement delay, we design an iterative DMPC scheme for nonlinear systems via Lyapunov-based control techniques. Sufficient conditions under which the proposed distributed MPC design guarantees that the state of the closed-loop system is ultimately bounded in a region that contains the origin are provided. The theoretical results are illustrated through a catalytic alkylation of benzene process example.

80Distributed output-feedback model predictive control for multi-agent consensusOpenAlex

David Copp, Kyriakos G. Vamvoudakis, João P. Hespanha

81Learning to Leverage Centralized and Distributed Strategies in Moving Horizon Model Predictive ControlOpenAlex

E.H. Cooper, Andrew Allman
Distributed model predictive control (DMPC) offers a computationally efficient alternative to centralized model predictive control (CMPC) for enabling the optimal control of industrial process systems. Both strategies offer distinct advantages: DMPC tends to reduce the computational burden of the control problem, thereby producing solutions on a time scale more suitable for real-time process control, whereas CMPC tends to yield higher-quality control decisions. In this work, we demonstrate that problem parameters, such as state measurements and set points, significantly influence the computational costs or solution time for solving the nonlinear programming (NLP) problem associated with the centralized optimal control problem. We show that DMPC is preferable when computational costs are high, while CMPC is more effective when the costs are low. To navigate the trade-offs between these strategies in online control, we employ machine learning classifiers to identify when a problem instance favors a particular solution strategy. We augment the traditional feedback control loop with these classifiers to strategically choose between CMPC and DMPC during the moving horizon of the control. By doing so, we show that leveraging the individual strengths of each approach improves the overall quality of process control compared to a strictly centralized or distributed strategy. We demonstrate the efficacy of the classifier-informed algorithm selection across two case study process systems.

82Optimal Control of Iron-Removal Systems Based on Off-Policy Reinforcement LearningOpenAlex

Ning Chen, Shuhan Luo, Jiayang Dai, et al.
The goethite iron-removal process is an important procedure to remove the iron ions from the zinc hydrometallurgy. However, as a coherent system with complex reaction mechanism, associated uncertainties, and interconnected adjacent reactors, it is difficult for the process to accurately control the ion concentration. Because a large amount of historical data can be obtained during the process, an optimal control algorithm based on off-policy reinforcement learning is proposed in this paper to overcome these difficulties. According to the historical data, the weights of neural network are learned offline, and the optimal control strategy is solved online. Firstly, a bounded function is introduced to define the maximum effect of the coherent system on the subsystem cost function and to extend the cost function of the nominal system, so that the decentralized guaranteed cost control problem can be expressed as the optimal control problem of the nominal system. Then, an approximate iterative control algorithm based on actor-critic structure is proposed. The actor and critic neural networks are used to approximate control strategies and cost functions respectively. To achieve complete off-line, a new neural network is added to the actor-critic structure to approximate a part of the unknown system structure, and the three neural network parameters are optimized by the state transition algorithm. Finally, the strategy update and strategy iteration operations are performed alternately to learn optimal control strategies. The effectiveness and flexibility of the proposed off-policy optimal control method is validated by data from a real industrial goethite iron-removal process.

83Design and Application of Distributed Economic Model Predictive Control for Large-Scale Building Temperature RegulationOpenAlex

Nishith R. Patel, James B. Rawlings, Michael Wenzel, et al.
Although recent research has suggested model predictive control as a promising solution for minimizing energy costs of commercial buildings, advanced control systems have not been widely deployed in practice. Large-scale implementations, including industrial complexes and university campuses, may contain thousands of air handler units each serving a multiplicity of zones. A single centralized control system for these applications is not desirable. In this paper, we propose a distributed control system to economically optimize temperature regulation for large-scale commercial building applications. The decomposition strategy considers the complexities of thermal energy storage, zone interactions, and chiller plant equipment while remaining computationally tractable. One of the primary benefits of the proposed formulation is that the low-level airside problem can be decoupled and solved in a distributed manner; hence, it can be easily extended to handle large applications. Peak demand charges, a major source of coupling, are included. The interactions of the airside system with the waterside system are also considered, including discrete decisions, such as turning chillers on and off. To deploy such a control scheme, a system model is required. Since using physical knowledge about building models can greatly reduce the number of parameters that must be identified, grey-box models are recommended to reduce the length of expensive identification testing. We demonstrate the effectiveness of this control system architecture and identification procedure via simulation studies.

84Hierarchically coordinated economic MPC plantwide control of mixed continuous‐batch units in process industries with application to a beet sugar plantOpenAlex

Rogelio Mazaeda, S. Cristea, César de Prada
Summary This paper deals with the optimal operation of processes that combine batch and continuous units. The proposed approach is based on a hierarchical architecture with two layers. The lower layer manages the optimal operation of the batch units in a noncentralized fashion, whereas the upper layer is concerned with the scheduling of the batch units and with their smooth integration with the continuous ones. The strategy has been applied to a challenging problem found at the interface of the fed‐batch crystallizers with the upstream evaporation section in beet sugar factories. The presented approach aims at designing a system that can effectively perform the plantwide economic optimization, specifically addressing the issue of energy efficiency, while complying with all process and operational constraints.

85Offset-free distributed predictive control based on fuzzy logic: Application to a real four-tank plantOpenAlex

Mario Francisco, Eva Masero, Keidy Morales-Rodelo, et al.
This paper proposes an offset-free distributed implementation of a model predictive controller that employs fuzzy negotiation between agents. The scheme is based on model augmentation with additional disturbances to enable zero-offset tracking. Moreover, we code the negotiation criteria as a set of suitable fuzzy rules and consider stability and feasibility guarantees in the controller design for the linearized subsystems. We applied the method to an experimental four-tank plant, showing its effectiveness despite the coupling between subsystems and system-model mismatch.

86Automatic decomposition of large-scale industrial processes for distributed MPC on the Shell–Yokogawa Platform for Advanced Control and Estimation (PACE)OpenAlex

Wentao Tang, Pierre Carrette, Yongsong Cai, et al.

87Efficient interior point methods for multistage problems arising in receding horizon controlOpenAlex

Alexander Domahidi, Aldo U. Zgraggen, Melanie N. Zeilinger, et al.
Receding horizon control requires the solution of an optimization problem at every sampling instant. We present efficient interior point methods tailored to convex multistage problems, a problem class which most relevant MPC problems with linear dynamics can be cast in, and specify important algorithmic details required for a high speed implementation with superior numerical stability. In particular, the presented approach allows for quadratic constraints, which is not supported by existing fast MPC solvers. A categorization of widely used MPC problem formulations into classes of different complexity is given, and we show how the computational burden of certain quadratic or linear constraints can be decreased by a low rank matrix forward substitution scheme. Implementation details are provided that are crucial to obtain high speed solvers.We present extensive numerical studies for the proposed methods and compare our solver to three well-known solver packages, outperforming the fastest of these by a factor 2-5 in speed and 3-70 in code size. Moreover, our solver is shown to be very efficient for large problem sizes and for quadratically constrained QPs, extending the set of systems amenable to advanced MPC formulations on low-cost embedded hardware.

88Fast computation of the quadratic programming subproblem in model predictive controlOpenAlex

Ruth Milman, E.J. Davidson
One of the main drawbacks of model predictive control (MPC) is that large MPC horizon times can cause requirements of excessive computational time to solve the quadratic programming (QP) minimization which occurs in the calculation of the controller at each sampling interval. This motivates the study of finding faster ways for computing the QP problem associated with MPC. In this paper, a new non-feasible active set method is proposed for solving the QP optimization problem that occurs in MPC, which can be some 10/spl times/ faster than conventional existing active set methods, and to a primal-dual interior point method, using six representative linearized industrial control system examples.

89An online active set strategy to overcome the limitations of explicit MPCOpenAlex

Hans Joachim Ferreau, H. G. Bock, Martin Diehl
Abstract Nearly all algorithms for linear model predictive control (MPC) either rely on the solution of convex quadratic programs (QPs) in real time, or on an explicit precalculation of this solution for all possible problem instances. In this paper, we present an online active set strategy for the fast solution of parametric QPs arising in MPC. This strategy exploits solution information of the previous QP under the assumption that the active set does not change much from one QP to the next. Furthermore, we present a modification where the CPU time is limited in order to make it suitable for strict real‐time applications. Its performance is demonstrated with a challenging test example comprising 240 variables and 1191 inequalities, which depends on 57 parameters and is prohibitive for explicit MPC approaches. In this example, our strategy allows CPU times of well below 100 ms per QP and was about one order of magnitude faster than a standard active set QP solver. Copyright © 2007 John Wiley &amp; Sons, Ltd.

90Fast Model Predictive Control Using Online OptimizationOpenAlex

Yang Wang, Stephen Boyd
A widely recognized shortcoming of model predictive control (MPC) is that it can usually only be used in applications with slow dynamics, where the sample time is measured in seconds or minutes. A well-known technique for implementing fast MPC is to compute the entire control law offline, in which case the online controller can be implemented as a lookup table. This method works well for systems with small state and input dimensions (say, no more than five), few constraints, and short time horizons. In this paper, we describe a collection of methods for improving the speed of MPC, using online optimization. These custom methods, which exploit the particular structure of the MPC problem, can compute the control action on the order of 100 times faster than a method that uses a generic optimizer. As an example, our method computes the control actions for a problem with 12 states, 3 controls, and horizon of 30 time steps (which entails solving a quadratic program with 450 variables and 1284 constraints) in around 5 ms, allowing MPC to be carried out at 200 Hz.

91Code generation for receding horizon controlOpenAlex

Jacob Mattingley, Yang Wang, Stephen Boyd
Receding horizon control (RHC), also known as model predictive control (MPC), is a general purpose control scheme that involves repeatedly solving a constrained optimization problem, using predictions of future costs, disturbances, and constraints over a moving time horizon to choose the control action. RHC handles constraints, such as limits on control variables, in a direct and natural way, and generates sophisticated feed-forward actions. The main disadvantage of RHC is that an optimization problem has to be solved at each step, which leads many control engineers to think that it can only be used for systems with slow sampling (say, less than one Hz). Several techniques have recently been developed to get around this problem. In one approach, called explicit MPC, the optimization problem is solved analytically and explicitly, so evaluating the control policy requires only a lookup table search. Another approach, which is our focus here, is to exploit the structure in the optimization problem to solve it efficiently. This approach has previously been applied in several specific cases, using custom, hand written code. However, this requires significant development time, and specialist knowledge of optimization and numerical algorithms. Recent developments in convex optimization code generation have made the task much easier and quicker. With code generation, the RHC policy is specified in a high-level language, then automatically transformed into source code for a custom solver. The custom solver is typically orders of magnitude faster than a generic solver, solving in milliseconds or microseconds on standard processors, making it possible to use RHC policies at kilohertz rates. In this paper we demonstrate code generation with two simple control examples. They show a range of problems that may be handled by RHC. In every case, we show a speedup of several hundred times from generic parser-solvers.

92High-performance small-scale solvers for linear Model Predictive ControlOpenAlex

Gianluca Frison, Hans Henrik Brandenborg Sørensen, Bernd Dammann, et al.
In Model Predictive Control (MPC), an optimization problem needs to be solved at each sampling time, and this has traditionally limited use of MPC to systems with slow dynamic. In recent years, there has been an increasing interest in the area of fast small-scale solvers for linear MPC, with the two main research areas of explicit MPC and tailored on-line MPC. State-of-the-art solvers in this second class can outperform optimized linear-algebra libraries (BLAS) only for very small problems, and do not explicitly exploit the hardware capabilities, relying on compilers for that. This approach can attain only a small fraction of the peak performance on modern processors. In our paper, we combine high-performance computing techniques with tailored solvers for MPC, and use the specific instruction sets of the target architectures. The resulting software (called HPMPC) can solve linear MPC problems 2 to 8 times faster than the current state-of-the-art solver for this class of problems, and the high-performance is maintained for MPC problems with up to a few hundred states.

93A Survey on Explicit Model Predictive ControlOpenAlex

Alessandro Alessio, Alberto Bemporad

94On-board Model Predictive Control of a Quadrotor Helicopter: Design, Implementation, and ExperimentsOpenAlex

Patrick Bouffard
This report describes work in applying model predictive control (MPC) techniques to the control of quadrotor helicopters, a type of micro aerial vehicle (MAV) platform that has gained great popularity in recent years both in research and commercial/military settings. MPC is a form of optimal control which is attractive in part because it allows engineering requirements to be addressed directly in the design of the controller in terms of costs to be minimized and constraints to be satisfied in an optimization problem. Furthermore, for many engineering problems of interest, the optimization to be performed is convex, meaning that a global optimum can be efficiently computed. MPC first found broad early application in the process industry, where the typically longer time scales were compatible with the time necessary to solve the optimization problem. More recently with both the exponential increase in available computing power and the development of more efficient solution techniques, MPC has become an option for control of systems with faster dynamics, such as quadrotors. We bring together results from our application of two distinct variants of MPC. The common thread is that we seek advanced control algorithms that can be applied to an autonomous MAV like the quadrotor, ideally without requiring any external resources, i.e. we aim to perform all computations required for real-time closed-loop control on-board the vehicle. The first variant is known as explicit MPC, where in a sense the heavy numerical work of solving optimization problems is done a priori and off-line, such that the on-line implementation requires minimal computation. In this report we describe the design and implementation of three explicit MPC controllers of increasing complexity, and experiments in which these controllers were executed on a quadrotor's on-board computer to control the vehicle in hovering flight. We describe the results of these experiments, with particular emphasis on the resulting performance, in terms of each controller's ability to maintain the quadrotor near a static hover condition. The second variant is learning-based model predictive control (LBMPC). LBMPC seeks to combine techniques from statistical learning which can help improve performance, with tools and concepts from control theory which provide guarantees about safety, robustness, and convergence. Prior to this work, LBMPC had been implemented in systems quite different from the quadrotor, such as an air-conditioning testbed. Our LBMPC controller for the quadrotor helps demonstrate the formulation's versatility, and some of the particulars of this problem required extensions to LBMPC which we describe. Our main focus here is on demonstrating properties of LBMPC controllers on the quadrotor testbed, with an implementation of LBMPC that runs in real-time on the quadrotor's on-board computer. Robustness to ?mis-learning? is one aspect of LBMPC that we demonstrate in an experiment where we deliberately mis-tune a learning algorithm. We also demonstrate the improvement in performance possible when a well-tuned learning algorithm is used, show learning used to update the model in a physically meaningful way, and demonstrate the use of the LBMPC controller in an integrated robotic task requiring speed and precision: we design a controller that enables the quadrotor to catch balls.

95Structure-Exploiting Numerical Algorithms for Optimal ControlOpenAlex

Isak Nielsen
Numerical algorithms for efficiently solving optimal control problems are important for commonly used advanced control strategies, such as model predictive control (MPC), but can also be useful for advanced estimation techniques, such as moving horizon estimation (MHE). In MPC, the control input is computed by solving a constrained finite-time optimal control (CFTOC) problem on-line, and in MHE the estimated states are obtained by solving an optimization problem that often can be formulated as a CFTOC problem. Common types of optimization methods for solving CFTOC problems are interior-point (IP) methods, sequential quadratic programming (SQP) methods and active-set (AS) methods. In these types of methods, the main computational effort is often the computation of the second-order search directions. This boils down to solving a sequence of systems of equations that correspond to unconstrained finite-time optimal control (UFTOC) problems. Hence, high-performing second-order methods for CFTOC problems rely on efficient numerical algorithms for solving UFTOC problems. Developing such algorithms is one of the main focuses in this thesis. When the solution to a CFTOC problem is computed using an AS type method, the aforementioned system of equations is only changed by a low-rank modification between two AS iterations. In this thesis, it is shown how to exploit these structured modifications while still exploiting structure in the UFTOC problem using the Riccati recursion. Furthermore, direct (non-iterative) parallel algorithms for computing the search directions in IP, SQP and AS methods are proposed in the thesis. These algorithms exploit, and retain, the sparse structure of the UFTOC problem such that no dense system of equations needs to be solved serially as in many other algorithms. The proposed algorithms can be applied recursively to obtain logarithmic computational complexity growth in the prediction horizon length. For the case with linear MPC problems, an alternative approach to solving the CFTOC problem on-line is to use multiparametric quadratic programming (mp-QP), where the corresponding CFTOC problem can be solved explicitly off-line. This is referred to as explicit MPC. One of the main limitations with mp-QP is the amount of memory that is required to store the parametric solution. In this thesis, an algorithm for decreasing the required amount of memory is proposed. The aim is to make mp-QP and explicit MPC more useful in practical applications, such as embedded systems with limited memory resources. The proposed algorithm exploits the structure from the QP problem in the parametric solution in order to reduce the memory footprint of general mp-QP solutions, and in particular, of explicit MPC solutions. The algorithm can be used directly in mp-QP solvers, or as a post-processing step to an existing solution.

96OSQP: an operator splitting solver for quadratic programsOpenAlex

Bartolomeo Stellato, Goran Banjac, Paul J. Goulart, et al.

97Software and Hardware Code Generation for Predictive Control Using Splitting MethodsOpenAlex

Harsh Shukla, B. G. Khusainov, Eric C. Kerrigan, et al.
This paper presents SPLIT, a C code generation tool for Model Predictive Control (MPC) based on operator splitting methods. In contrast to existing code generation packages, SPLIT is capable of generating both software and hardware-oriented C code to allow quick prototyping of optimization algorithms on conventional CPUs and field-programmable gate arrays (FPGAs). A Matlab interface is provided for compatibility with existing commercial and open-source software packages. A numerical study compares software, hardware and heterogeneous implementations of splitting methods and investigates MPC design trade-offs. For the considered testcases the reported speedup of hardware implementations over software realizations is 3x to 11x.

98Constrained LQR using online decomposition techniquesOpenAlex

Laura Ferranti, Giorgos Stathopoulos, Colin N. Jones, et al.
This paper presents an algorithm to solve the infinite horizon constrained linear quadratic regulator (CLQR) problem using operator splitting methods. First, the CLQR problem is reformulated as a (finite-time) model predictive control (MPC) problem without terminal constraints. Second, the MPC problem is decomposed into smaller subproblems of fixed dimension independent of the horizon length. Third, using the fast alternating minimization algorithm to solve the subproblems, the horizon length is estimated online, by adding or removing subproblems based on a periodic check on the state of the last subproblem to determine whether it belongs to a given control invariant set. We show that the estimated horizon length is bounded and that the control sequence computed using the proposed algorithm is an optimal solution of the CLQR problem. Compared to state-of-the-art algorithms proposed to solve the CLQR problem, our design solves at each iteration only unconstrained least-squares problems and simple gradient calculations. Furthermore, our technique allows the horizon length to decrease online (a useful feature if the initial guess on the horizon is too conservative). Numerical results on a planar system show the potential of our algorithm.

99Efficiently Solving the Harmonic Model Predictive Control FormulationOpenAlex

Pablo Krupa, Daniel Limón, Alberto Bemporad, et al.
Harmonic model predictive control (HMPC) is a model predictive control (MPC) formulation that displays several benefits over other MPC formulations, especially when using a small prediction horizon. These benefits, however, come at the expense of an optimization problem that is no longer the typical quadratic programming problem derived from most linear MPC formulations due to the inclusion of a particular class of second-order cone constraints. This article presents a method for efficiently dealing with these constraints in operator splitting methods, leading to a computation time for solving HMPC in line with state-of-the-art solvers for linear MPC. We show how to apply this result to the alternating direction method of the multipliers algorithm, presenting a solver that we compare against other solvers from the literature, including solvers for other linear MPC formulations. The results show that the proposed solver, and by extension the HMPC formulation, is suitable for its implementation in embedded systems.

100Multistep Model Predictive Control for Electrical Drives—A Fast Quadratic Programming SolutionOpenAlex

Haotian Xie, Jianming Du, Dongliang Ke, et al.
Due to its merits of fast dynamic response, flexible inclusion of constraints and the ability to handle multiple control targets, model predictive control has been widely applied in the symmetry topologies, e.g., electrical drive systems. Predictive current control is penalized by the high current ripples at steady state because only one switching state is employed in every sampling period. Although the current quality can be improved at a low switching frequency by the extension of the prediction horizon, the number of searched switching states will grow exponentially. To tackle the aforementioned issue, a fast quadratic programming solver is proposed for multistep predictive current control in this article. First, the predictive current control is described as a quadratic programming problem, in which the objective function is rearranged based on the current derivatives. To avoid the exhaustive search, two vectors close to the reference derivative are preselected in every prediction horizon. Therefore, the number of searched switching states is significantly reduced. Experimental results validate that the predictive current control with a prediction horizon of 5 can achieve an excellent control performance at both steady state and transient state while the computational time is low.

101Efficient parallel coordinate descent algorithm for convex optimization problems with separable constraints: Application to distributed MPCOpenAlex

Ion Necoara, Dragos Clipici

102Parallel move blocking Model Predictive ControlOpenAlex

Stefano Longo, Eric C. Kerrigan, Keck Voon Ling, et al.
This paper proposes the use of parallel computing architectures (multi-core, FPGA, GPU) to implement a parallel move blocking Model Predictive Control (MPC) algorithm where multiple, but smaller optimization problems are solved simultaneously. Since these problems are solved in parallel, the computational delay is reduced when compared to standard MPC. This allows for faster sampling that can outperform, in terms of closed-loop cost, a standard MPC formulation. Feasibility and stability are guaranteed by an appropriate selection of so-called blocking matrices.

103Secure and Provenance Enhanced Internet of Health Things Framework: A Blockchain Managed Federated Learning ApproachOpenAlex

Md. Abdur Rahman, M. Shamim Hossain, Mohammad Saiful Islam, et al.
Recent advancements in the Internet of Health Things (IoHT) have ushered in the wide adoption of IoT devices in our daily health management. For IoHT data to be acceptable by stakeholders, applications that incorporate the IoHT must have a provision for data provenance, in addition to the accuracy, security, integrity, and quality of data. To protect the privacy and security of IoHT data, federated learning (FL) and differential privacy (DP) have been proposed, where private IoHT data can be trained at the owner's premises. Recent advancements in hardware GPUs even allow the FL process within smartphone or edge devices having the IoHT attached to their edge nodes. Although some of the privacy concerns of IoHT data are addressed by FL, fully decentralized FL is still a challenge due to the lack of training capability at all federated nodes, the scarcity of high-quality training datasets, the provenance of training data, and the authentication required for each FL node. In this paper, we present a lightweight hybrid FL framework in which blockchain smart contracts manage the edge training plan, trust management, and authentication of participating federated nodes, the distribution of global or locally trained models, the reputation of edge nodes and their uploaded datasets or models. The framework also supports the full encryption of a dataset, the model training, and the inferencing process. Each federated edge node performs additive encryption, while the blockchain uses multiplicative encryption to aggregate the updated model parameters. To support the full privacy and anonymization of the IoHT data, the framework supports lightweight DP. This framework was tested with several deep learning applications designed for clinical trials with COVID-19 patients. We present here the detailed design, implementation, and test results, which demonstrate strong potential for wider adoption of IoHT-based health management in a secure way.

104A Comprehensive Review of Big Data Intelligent Decision-Making Models for Smart FarmsOpenAlex

Chang Qin, Peiqin Zhao, Ying Qian, et al.
Big data and artificial intelligence technologies are driving a paradigm shift in smart farming, yet intelligent decision-making faces critical bottlenecks. At the data level, challenges include fragmentation, high acquisition costs, and inadequate secure sharing; at the model level, issues involve regional heterogeneity, weak adaptability, and insufficient explainability. To address these, this paper systematically reviews global research to establish a theoretical framework spanning the entire production cycle. Regarding data governance, trends favor federated systems with unified metadata and layered storage, utilizing technologies like federated learning for secure lifecycle management. For decision-making, approaches are evolving from experience-based to data-driven intelligence. Pre-harvest planning now integrates mechanistic models and transfer learning for suitability and variety optimization. In-season management leverages deep reinforcement learning (DRL) and model predictive control (MPC) for precise regulation of seedlings, water, fertilizer, and pests. Post-harvest evaluation strategies utilize spatio-temporal deep learning architectures (e.g., Transformers or LSTMs) and intelligent optimization algorithms for yield prediction and machinery scheduling. Finally, a staged development pathway is proposed: prioritizing standardized data governance and foundation models in the short term; advancing federated learning and human–machine collaboration in the mid-term; and achieving real-time, ethical edge AI in the long term. This framework supports the transition toward precise, transparent, and sustainable smart agriculture.

105Microgrids with Model Predictive Control: A Critical ReviewOpenAlex

Karan Singh Joshal, Neeraj Gupta
Microgrids face significant challenges due to the unpredictability of distributed generation (DG) technologies and fluctuating load demands. These challenges result in complex power management systems characterised by voltage/frequency variations and intricate interactions with the utility grid. Model predictive control (MPC) has emerged as a powerful technique to effectively address these challenges. By applying a receding horizon control strategy, MPC offers promising solutions for optimising constraints and enhancing microgrid operations. The purpose of this review paper is to comprehensively analyse the application of MPC in microgrids, covering various levels of the hierarchical control structure. Furthermore, this paper explores the emerging trend of employing MPC across microgrid applications, ranging from converter control levels for power quality to overarching energy management systems. It also investigates the future research perspectives by considering the challenges associated with establishing MPC-based microgrid control. The key conclusion derived from this review paper is that the implementation of MPC techniques in microgrid operations can greatly improve their overall performance, efficiency, and resilience. This paper thoroughly examines the various challenges faced in MPC-based microgrid operations, underscoring the significance of conducting research in advanced artificial intelligence (AI)-based MPC methods. It highlights how these cutting-edge AI techniques can bring about economic benefits in microgrid operations, addressing the complex demands of efficient energy management in a rapidly evolving landscape. The presented insights strive to enhance the comprehension and adoption of MPC techniques in microgrid settings, actively contributing to the ongoing improvement of their operational processes. By shedding light on key aspects and offering valuable guidance, this work aims to propel the advancement and effective utilisation of MPC methodologies in microgrids, ultimately leading to optimised performance and enhanced overall operations.

106Towards Sustainable Buildings and Energy Communities: AI-Driven Transactive Energy, Smart Local Microgrids, and Life Cycle IntegrationOpenAlex

Andrzej Ożadowicz
The transition towards sustainable and low-carbon energy systems highlights the crucial role of buildings, microgrids, and local communities as key actors in enhancing resilience and achieving decarbonization targets. The application of artificial intelligence (AI) is of paramount importance as it enables accurate prediction, adaptive control, and optimization of distributed resources. This paper reviews recent advances in AI applications for transactive energy (TE) and dynamic energy management (DEM), focusing on their integration with building automation, microgrid coordination, and community energy exchanges. It also considers the emerging role of life cycle-based methods, such as life cycle assessment (LCA) and life cycle cost (LCC), in extending operational intelligence to long-term environmental and economic objectives. The analysis is based on a curated set of 97 publications identified through structured queries and thematic filtering. The findings indicate substantial advancement in methodological approaches, notably reinforcement learning (RL), hybrid model predictive control, federated and edge AI, and digital twin applications. However, this study also uncovers shortcomings in the integration and interoperability of sustainability. This paper contributes by consolidating fragmented research and proposing a multi-layered AI framework that aligns short-term performance with long-term resilience and sustainability.

107Real-Time Neural MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic PlatformsOpenAlex

Tim Salzmann, Elia Kaufmann, Jon Arrizabalaga, et al.
Model Predictive Control (MPC) has become a popular framework in embedded control for high-performance autonomous systems. However, to achieve good control performance using MPC, an accurate dynamics model is key. To maintain real-time operation, the dynamics models used on embedded systems have been limited to simple first-principle models, which substantially limits their representative power. In contrast to such simple models, machine learning approaches, specifically neural networks, have been shown to accurately model even complex dynamic effects, but their large computational complexity hindered combination with fast real-time iteration loops. With this work, we present <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Real-time Neural MPC</i> , a framework to efficiently integrate large, complex neural network architectures as dynamics models within a model-predictive control pipeline. Our experiments, performed in simulation and the real world onboard a highly agile quadrotor platform, demonstrate the capabilities of the described system to run learned models with, previously infeasible, large modeling capacity using gradient-based online optimization MPC. Compared to prior implementations of neural networks in online optimization MPC we can leverage models of over 4000 times larger parametric capacity in a 50 Hz real-time window on an embedded platform. Further, we show the feasibility of our framework on real-world problems by reducing the positional tracking error by up to 82% when compared to state-of-the-art MPC approaches without neural network dynamics.

108Approximate model predictive building control via machine learningOpenAlex

Ján Drgoňa, Damien Picard, Michal Kvasnica, et al.
Many studies have proven that the building sector can significantly benefit from replacing the current practice rule-based controllers (RBC) by more advanced control strategies like model predictive control (MPC). However, the optimization-based control algorithms, like MPC, impose increasing hardware and software requirements, together with more complicated error handling capabilities required from the commissioning staff. In recent years, several studies introduced promising remedy for these problems by using machine learning algorithms. The idea is based on devising simplified control laws learned from MPC. The main advantage of the proposed methods stems from their easy implementation even on low-level hardware. However, most of the reported studies were dealing only with problems with a limited complexity of the parametric space, and devising laws only for a single control variable, which inevitably limits their applicability to more complex building control problems. In this paper, we introduce a versatile framework for synthesis of simple, yet well-performing control strategies that mimic the behavior of optimization-based controllers, also for large scale multiple-input-multiple-output (MIMO) control problems which are common in the building sector. The approach employs multivariate regression and dimensionality reduction algorithms. Particularly, deep time delay neural networks (TDNN) and regression trees (RT) are used to derive the dependency of multiple real-valued control inputs on parameters. The complexity of the problem, as well as implementation cost, are further reduced by selecting the most significant features from the set of parameters. This reduction is based on straightforward manual selection, principal component analysis (PCA) and dynamic analysis of the building model. The approach is demonstrated on a case study employing temperature control in a six-zone building, described by a linear model with 286 states and 42 disturbances, resulting in an MPC problem with more than thousand of parameters. The results show that simplified control laws retain most of the performance of the complex MPC, while significantly decreasing the complexity and implementation cost.

109Bi-Level Optimization Augmented with Conditional Variational Autoencoder for Autonomous Driving in Dense TrafficOpenAlex

Arun Singh, Jatan Shrestha, Nicola Albarella
Autonomous driving has a natural bi-level structure. The goal of the upper behavioural layer is to provide appropriate lane change, speeding up, and braking decisions to optimize a given driving task. However, this layer can only indirectly influence the driving efficiency through the lower-level trajectory planner, which takes in the behavioural inputs to produce motion commands. Existing sampling-based approaches do not fully exploit the strong coupling between the behavioural and planning layer. On the other hand, end-to-end Reinforcement Learning (RL) can learn a behavioural layer while incorporating feedback from the lower-level planner. However, purely data-driven approaches often fail in safety metrics in unseen environments. This paper presents a novel alternative; a parameterized bi-level optimization that jointly computes the optimal behavioural decisions and the resulting downstream trajectory. Our approach runs in real-time using a custom GPU-accelerated batch optimizer and a Conditional Variational Autoencoder (CVAE) learnt warm-start strategy. Extensive simulations show that our approach outperforms state-of-the-art Model Predictive Control (MPC) and RL approaches in terms of collision rate while being competitive in driving efficiency.

110Data-Driven Modeling and Distributed Predictive Control of Mixed Vehicle PlatoonsOpenAlex

Jingyuan Zhan, Zibo Ma, Liguo Zhang
With the development of automatic driving technology and the internet of vehicles, platooning based on control of connected autonomous vehicles has become one of the most promising approaches to improve traffic efficiency. This paper studies the control problem of mixed vehicle platoons consisting of human-driven vehicles and connected autonomous vehicles. Firstly, we propose a data-driven method to model mixed vehicle platoons based on Koopman operator theory. This method gives a way to represent the mixed vehicle platoon by a linear model in a high-dimensional space, the approximation of which is obtained by a neural network framework. Secondly, we employ model predictive control (MPC) to address the platoon control problem of mixed vehicle platoons, where both centralized MPC and distributed MPC algorithms are designed. Finally, the effectiveness of the data-driven modeling method and the centralized/distributed MPC algorithms is verified by numerical simulations. It is revealed that the proposed data-driven DMPC algorithm exhibits comparable control performance with less computation cost compared with the centralized MPC algorithm, and it shows faster convergence speed than the nonlinear model based DMPC algorithm.

111Comparison of Deep Reinforcement Learning and Model Predictive Control for Adaptive Cruise ControlOpenAlex

Yuan Lin, John McPhee, Nasser L. Azad
This study compares Deep Reinforcement Learning (DRL) and Model Predictive Control (MPC) for Adaptive Cruise Control (ACC) design in car-following scenarios. A first-order system is used as the Control-Oriented Model (COM) to approximate the acceleration command dynamics of a vehicle. Based on the equations of the control system and the multi-objective cost function, we train a DRL policy using Deep Deterministic Policy Gradient (DDPG) and solve the MPC problem via Interior-Point Optimization (IPO). Simulation results for the episode costs show that, when there are no modeling errors and the testing inputs are within the training data range, the DRL solution is equivalent to MPC with a sufficiently long prediction horizon. Particularly, the DRL episode cost is only 5.8% higher than the benchmark optimal control solution provided by optimizing the entire episode via IPO. The DRL control performance degrades when the testing inputs are outside the training data range, indicating inadequate machine learning generalization. When there are modeling errors due to control delay, disturbances, and/or testing with a High-Fidelity Model (HFM) of the vehicle, the DRL-trained policy performs better when the modeling errors are large while having similar performances as MPC when the modeling errors are small.

112Data-driven torque and pitch control of wind turbines via reinforcement learningOpenAlex

Jingjie Xie, Hongyang Dong, Xiaowei Zhao
This paper addresses the torque and pitch control problems of wind turbines. The main contribution of this work is the development of an innovative reinforcement learning (RL)-based control method targeting wind turbine applications. Our RL-based control framework synergistically combines the advantages of deep neural networks (DNNs) and model predictive control (MPC) technologies. The proposed control strategy is data-driven, adapting to real-time changes in system dynamics and enhancing control performance and robustness. Additionally, the incorporation of an MPC structure within our design improves learning efficiency and reduces the high computational complexity typically found in deep RL algorithms. Specifically, a DNN is designed to approximate the wind turbine dynamics based on a continuously updated dataset composed of state and action measurements taken at specified sampling intervals. The real-time control policy is generated by integrating the online trained DNN into an MPC architecture. The proposed method iteratively updates the DNN and control policy in real-time to optimize performance. As a primary result of this work, the proposed method demonstrates superior robustness and control performance compared to commonly-employed MPC and other baseline wind turbine controllers in the presence of uncertainties and unexpected actuator faults. This effectiveness is showcased through simulations with a high-fidelity wind turbine simulator.

113A Coordinated Optimal Operation of a Grid-Connected Wind-Solar Microgrid Incorporating Hybrid Energy Storage Management SystemsOpenAlex

Muhammad Bakr Abdelghany, Ahmed Al‐Durra, Fei Gao
The hybrid-energy storage systems (ESSs) are promising eco-friendly power converter devices used in a wide range of applications. However, their insufficient lifespan is one of the key issues by hindering their large-scale commercial application. In order to extend the lifespan of the hybrid-ESSs, the cost functions proposed in this paper include the degradation of the hydrogen devices and the battery. Indeed, this paper aims to develop a sophisticated model predictive control strategy for a grid-connected wind and solar microgrid, which includes a hydrogen-ESS, a battery-ESS, and the interaction with external consumers, e.g., battery/fuel cell electric vehicles. The integrated system requires the management of its energy production in different forms, i.e., the electric and the hydrogen ones. The proposed strategy consists of the economical and operating costs of the hybrid-ESSs, the degradation issues, and the physical and dynamic constraints of the system. The mixed-logic dynamic framework is required to model the operating modes of the hybrid-ESSs and the switches between them. The effectiveness of the controller is analyzed by numerical simulations which are conducted using solar and wind generation profiles of solar panels and wind farms located in Abu Dhabi, United Arab Emirates. Such simulations, indeed, show that the proposed strategy appropriately manages the plant by fulfilling constraints and energy requests while reducing device costs and increasing battery life.

114Building Energy Management With Reinforcement Learning and Model Predictive Control: A SurveyOpenAlex

Huiliang Zhang, Sayani Seal, Di Wu, et al.
Building energy management has been recognized as of significant importance on improving the overall system efficiency and reducing the greenhouse gas emission. However, the building energy management system is now facing more challenges and uncertainties with the increasing penetration of renewable energy and increasing adoption of different types of electrical appliances and equipment. Classical model predictive control (MPC) has shown effective in building energy management, although it suffers from labour-intensive modelling and complex online control optimization. Recently, with the growing accessibility to building control and automation data, data-driven solutions such as data-driven MPC and reinforcement learning (RL)-based methods have attracted more research interest. However, the potential of integrating these two types of methods and how to choose suitable control algorithms have not been well discussed. In this work, we first present a compact review of the recent advances in data-driven MPC and RL-based control methods for building energy management. Furthermore, the main challenges in these approaches and general discussions on the selection of control methods are discussed.

115Energy modelling and control of building heating and cooling systems with data-driven and hybrid models—A reviewOpenAlex

Yasaman Balali, Adrian Chong, Andrew Busch, et al.
Implementing an efficient control strategy for heating, ventilation, and air conditioning (HVAC) systems can lead to improvements in both energy efficiency and thermal performance in buildings. As HVAC systems and buildings are complicated dynamic systems, the effectiveness of both data-driven and model-based control methods has been widely investigated by researchers. However, the main challenges that impede the practical application of model-based methods in real buildings are their reliance on the precision of control-oriented models and the dependence of data-based systems on the quantity and quality of input–output data. The objectives of this study are: (1) To present an overview of the prevalent thermal modelling strategies used as control-oriented models or virtual environments in model-based and data-based control methods, addressing the main requirements of thermal models; (2) the state-of-the-art of MPC and RL control techniques; (3) the data requirements for thermal models. The findings emphasise the need for unified guidelines to validate and verify the proposed control methods, ensuring their practical implementation in real buildings. Moreover, the inclusion of occupancy forecasts in models presents challenges due to the intricate nature of accurately predicting human behaviour, occupancy patterns, and their effects on thermal dynamics. Balancing thermal comfort and energy efficiency in HVAC systems with a supervisory controller remains a difficult task, but combining data-driven and physics-based models can help overcome challenges. Further research is needed to compare the effectiveness of MPC and RL approaches, and accurately measuring the impact of human behaviour and occupancy remains a significant obstacle.

116Robust constrained model predictive control using linear matrix inequalitiesOpenAlex

Mayuresh V. Kothare, V. Balakrishnan, Manfred Morari

117Robust Model Predictive Control via Scenario OptimizationOpenAlex

Giuseppe C. Calafiore, Lorenzo Fagiano
This paper discusses a novel probabilistic approach for the design of robust model predictive control (MPC) laws for discrete-time linear systems affected by parametric uncertainty and additive disturbances. The proposed technique is based on the iterated solution, at each step, of a finite-horizon optimal control problem (FHOCP) that takes into account a suitable number of randomly extracted scenarios of uncertainty and disturbances, followed by a specific command selection rule implemented in a receding horizon fashion. The scenario FHOCP is always convex, also when the uncertain parameters and disturbance belong to nonconvex sets, and irrespective of how the model uncertainty influences the system's matrices. Moreover, the computational complexity of the proposed approach does not depend on the uncertainty/disturbance dimensions, and scales quadratically with the control horizon. The main result in this work is related to the analysis of the closed loop system under receding-horizon implementation of the scenario FHOCP, and essentially states that the devised control law guarantees constraint satisfaction at each step with some a priori assigned probability <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> , while the system's state reaches the target set either asymptotically, or in finite time with probability at least <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> . The proposed method may be a valid alternative when other existing techniques, either deterministic or stochastic, are not directly usable due to excessive conservatism or to numerical intractability caused by lack of convexity of the robust or chance-constrained optimization problem.

118Robust Model Predictive Control via Scenario OptimizationOpenAlex

G. C. Calafiore, Lorenzo Fagiano
This paper discusses a novel probabilistic approach for the design of robust model predictive control (MPC) laws for discrete-time linear systems affected by parametric uncertainty and additive disturbances. The proposed technique is based on the iterated solution, at each step, of a finite-horizon optimal control problem (FHOCP) that takes into account a suitable number of randomly extracted scenarios of uncertainty and disturbances, followed by a specific command selection rule implemented in a receding horizon fashion. The scenario FHOCP is always convex, also when the uncertain parameters and disturbance belong to non-convex sets, and irrespective of how the model uncertainty influences the system's matrices. Moreover, the computational complexity of the proposed approach does not depend on the uncertainty/disturbance dimensions, and scales quadratically with the control horizon. The main result in this paper is related to the analysis of the closed loop system under receding-horizon implementation of the scenario FHOCP, and essentially states that the devised control law guarantees constraint satisfaction at each step with some a-priori assigned probability p, while the system's state reaches the target set either asymptotically, or in finite time with probability at least p. The proposed method may be a valid alternative when other existing techniques, either deterministic or stochastic, are not directly usable due to excessive conservatism or to numerical intractability caused by lack of convexity of the robust or chance-constrained optimization problem

119A tractable approximation of chance constrained stochastic MPC based on affine disturbance feedbackOpenAlex

Frauke Oldewurtel, Colin N. Jones, Manfred Morari
This paper deals with model predictive control of uncertain linear discrete-time systems with polytopic constraints on the input and chance constraints on the states. When having polytopic constraints and bounded disturbances, the robust problem with an open-loop prediction formulation is known to be conservative. Recently, a tractable closed-loop prediction formulation was introduced, which can reduce the conservatism of the robust problem. We show that in the presence of chance constraints and stochastic disturbances, this closed-loop formulation can be used together with a tractable approximation of the chance constraints to further increase the performance while satisfying the chance constraints with the predefined probability.

120Ultra-Local Model-Free Predictive Current Control Based on Nonlinear Disturbance Compensation for Permanent Magnet Synchronous MotorOpenAlex

Lingliang Xu, Guiming Chen, Qiaoyang Li
During motor operation, the motor parameters change, which causes parameter drift. They are also affected by internal and external unknown disturbances, which lead to reduced motor control performance, poor anti-interference performance, and low robustness. A method termed ultra-local model-free predictive current control (MFPCC) has previously been proposed to solve this problem; it uses only the input and output of the system and does not involve any motor parameters, because of which it is free of problems caused by model mismatch. However, the conventional MFPCC method requires adjustment of several control parameters and the estimated value of the total disturbance of the system has a certain deviation and a large pulsation, which result in obvious chattering of the motor output, low stability, reduced anti-interference performance, and low robustness. Therefore, this paper proposes an MFPCC method based on nonlinear disturbance compensation (NDC). This method does not involve any motor parameters, and it can more accurately and stably estimate the total system disturbance, and feedforward compensation, real-time update control information, only need to adjust two control parameters, the workload is small. Simulation results show that the proposed control method has high anti-interference performance, high robustness, small output ripple, and improved dynamic characteristics and that it can estimate the system disturbance accurately and stably.

121Model Predictive Control Based on Parametric Disturbance CompensationOpenAlex

Lingliang Xu, Guiming Chen, Guangshuai Li, et al.
Model predictive control (MPC) has been widely implemented in the motor because of its simple control design and good results. However, MPC relies on the permanent magnet synchronous motor (PMSM) system model. With the operation of the motor, parameter drift will occur due to temperature rise and flux saturation, resulting in model mismatch, which will seriously affect the control accuracy of the motor. This paper proposes a model predictive control based on parameter disturbance compensation that monitors system disturbances caused by motor parameter drift and performs real-time parameter disturbance compensation. And the frequency-domain method was used to analyze the convergence and filterability of the model. The Bode diagram of measurement error and input disturbance was studied when the parameters were underdamped, critically damped, and overdamped. Guidelines for parameter selection are given. Simulation results show that the proposed method has good dynamic performance, anti-interference ability, and parameter robustness, which effectively avoids the current static difference and oscillation problems caused by parameter changes.

122Robust tube-based MPC for tracking of constrained linear systems with additive disturbancesOpenAlex

Daniel Limón, I. Alvarado, Teodoro Álamo, et al.

123Robust Model Predictive Control with a Reactive Safety ModeOpenAlex

John M. Carson
Control algorithms suitable for online implementation in engineering applications, such as aerospace and mechanical vehicles, often require adherence to physical state and control constraints. Additionally, the chosen algorithms must provide robustness to uncertainty affecting both the system dynamics and the constraints. As further autonomy is built into these systems, the algorithms must be capable of blending multiple operational modes without violating the intrinsic constraints. Further, for real-time applications, the implemented control algorithms must be computationally efficient and reliable. The research in this thesis approaches these application needs by building upon the framework of MPC (Model Predictive Control). The MPC algorithm makes use of a nominal dynamics model to predict and optimize the response of a system under the application of a feedforward control policy, which is computed online in a finite-horizon optimization problem. The MPC algorithm is quite general and can be applied to linear and nonlinear systems and include explicit state and control constraints. The finite-horizon optimization is advantageous given the finite online computational capabilities in practical applications. Further, recursively re-solving the finite-horizon optimization in a compressing- or receding-horizon manner provides a form of closed-loop control that updates the feedforward control policy by setting the nominal state at re-solve to the current actual state. However, uncertainty between the nominal model and the actual system dynamics, along with constraint uncertainty can cause feasibility, and hence, robustness issues with the traditional MPC algorithm. In this thesis, an R-MPC (Robust and re-solvable MPC) algorithm is developed for uncertain nonlinear systems to address uncertainty affecting the dynamics. The R-MPC control policy consists of two components: the feedforward component that is solved online as in traditional MPC; and a separate feedback component that is determined offline, based on a characterization of the uncertainty between the nominal model and actual system. The addition of the feedback policy generates an invariant tube that ensures the actual system trajectories remain in the proximity of the nominal feedforward trajectory for all time. Further, this tube provides a means to theoretically guarantee continued feasibility and thus re-solvability of the R-MPC algorithm, both of which are required to guarantee asymptotic stability. To address uncertainty affecting the state constraints, an SR-MPC (Safety-mode augmented R-MPC) algorithm is developed that blends a reactive safety mode with the R-MPC algorithm for uncertain nonlinear systems. The SR-MPC algorithm has two separate operational modes: standard mode implements a modified version of the R-MPC algorithm to ensure asymptotic convergence to the origin; safety mode, if activated, guarantees containment within an invariant set about a safety reference for all time. The standard mode modifies the R-MPC algorithm with a special constraint to ensure safety-mode availability at any time. The safety-mode control is provided by an offline designed control policy that can be activated at any time during standard mode. The separate, reactive safety mode provides robustness to unexpected state-constraint changes; e.g., other vehicles crossing/stopping in the feasible path, or unexpected ground proximity in landing scenarios. Explicit design methods are provided for implementation of the R-MPC and SR-MPC algorithms on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives. Further, a discrete SR-MPC algorithm is developed that is more broadly applicable to real engineering systems. The discrete algorithm is formulated as a second-order cone program that can be solved online in a computationally efficient manner by using interior-point algorithms, which provide convergence guarantees in finite time to a prescribed level of accuracy. This discrete SR-MPC algorithm is demonstrated in simulation of a spacecraft descent toward a small asteroid where there is an uncertain gravity model, as well as errors in the expected surface altitude. Further, realistic effects such as control-input uncertainty, sensor noise, and unknown disturbances are included to further demonstrate the applicability of the discrete SR-MPC algorithm in a realistic implementation.

124Robust constrained tension control for high-precision roll-to-roll processes.PubMed

Zhiyi Chen, Boning Qu, Baoyang Jiang, et al.
ISA Trans. 2023 May;136:651-662. doi: 10.1016/j.isatra.2022.11.020. Epub 2022 Nov 26.
Tension control is critical for maintaining good product quality in most roll-to-roll (R2R) production systems. Previous work has primarily focused on improving the disturbance rejection performance of tension controllers. Here, a robust linear parameter-varying model predictive control (LPV-MPC) scheme is designed to enhance the tension tracking performance of a pilot R2R system for deposition of materials used in flexible thin film applications. The performance of a tension controller may degrade due to disturbances associated with model uncertainties and the slowly-changing dynamics in R2R systems. We introduce a method that separately treats these two sources of disturbance. The controller utilizes an incremental model to eliminate the errors caused by the mismatch between the nominal model and the actual system. A tube-based MPC formulation combined with scheduled parameters adequately updates models and corrects for the time-varying dynamics. Constraints on the rated motor torque are incorporated in the MPC to maintain the controller reliability and avoid machine failures. We illustrate the operation of our control algorithm through simulation of an actual R2R system. The controller outperforms the benchmarks in terms of fast transient response and offset-free tension tracking. It also demonstrates immunity from variations due to parametric uncertainties.

125Model Predictive Control Classical, Robust and StochasticOpenAlex

B. Kouvaritakis, Mark Cannon

126Robust and optimal predictive control of the COVID-19 outbreakOpenAlex

Johannes Köhler, Lukas Schwenkel, Anne Koch, et al.

127Model Predictive Trajectory Optimization and Control for Autonomous Surface Vessels Considering Traffic RulesOpenAlex

Anastasios Tsolakis, Rudy R. Negenborn, Vasso Reppa, et al.
This paper presents a rule-compliant trajectory optimization method for the guidance and control of Autonomous Surface Vessels. The method builds on Model Predictive Contouring Control and incorporates the International Regulations for Preventing Collisions at Sea relevant to motion planning. We use these rules for traffic situation assessment and to derive traffic-related constraints that are inserted in the optimization problem. Our optimization-based approach enables the formalization of abstract verbal expressions, such as traffic rules, and their incorporation in the trajectory optimization algorithm along with the dynamics and other constraints that dictate the system’s evolution over a sufficiently long planning horizon. The ability to plan considering different types of constraints and the system’s dynamics, over a long horizon in a unified manner, leads to a proactive motion planner that mimics rule-compliant maneuvering behavior, suitable for navigation in mixed-traffic environments. The efficacy and scalability of the derived algorithm are validated in different simulation scenarios, including complex traffic situations with multiple Obstacle Vessels.

128Path Planning and Tracking for Vehicle Collision Avoidance Based on Model Predictive Control With MulticonstraintsOpenAlex

Jie Ji, Amir Khajepour, Wael William Melek, et al.
A path planning and tracking framework is presented to maintain a collision-free path for autonomous vehicles. For path-planning approaches, a 3-D virtual dangerous potential field is constructed as a superposition of trigonometric functions of the road and the exponential function of obstacles, which can generate a desired trajectory for collision avoidance when a vehicle collision with obstacles is likely to happen. Next, to track the planned trajectory for collision avoidance maneuvers, the path-tracking controller formulated the tracking task as a multiconstrained model predictive control (MMPC) problem and calculated the front steering angle to prevent the vehicle from colliding with a moving obstacle vehicle. Simulink and CarSim simulations are conducted in the case where moving obstacles exist. The simulation results show that the proposed path-planning approach is effective for many driving scenarios, and the MMPC-based path-tracking controller provides dynamic tracking performance and maintains good maneuverability.

129Nonlinear Model Predictive Control for trajectory tracking and collision avoidance of underactuated vessels with disturbancesOpenAlex

Mohamed Abdelaal, Martin Fränzle, Axel Hahn

130An MPC-Based Approach to Provable System-Wide Safety and Liveness of Autonomous Ground TrafficOpenAlex

Kyoung-Dae Kim, P. R. Kumar
An important area of cyber-physical systems research is the development of smart ground transportation systems due to their potentially significant impact on safety, the economy, and the environment. We propose an approach based on model predictive control (MPC) for the development of provably collision free autonomous ground transportation systems, and present an autonomous intersection management framework. The MPC approach enables a vehicle to generate its own motion locally in time based on an optimization framework, incorporating constraints based on the states of other vehicles in the neighborhood, the speed limit of a road, the maximum values of acceleration and deceleration, etc. Safety and liveness of the traffic are however system-wide properties, not merely neighborhood properties, and the challenge is to augment this distributed optimization with coordination rules that guarantee overall system-wide safety as well as liveness of the traffic. We design two vehicle-to-vehicle (V2V) coordination rules, along with a vehicle-to-infrastructure rule, and establish the system-wide safety and liveness of the autonomous traffic based on each vehicle's MPC motion planner, operating in conjunction with an algorithm that orders vehicles according to their runtime properties. We also conduct a comparative simulation study of the throughput performance at an intersection of the above approach against another popular algorithm, the All-Way STOP.

131Model Predictive Contouring Control for Collision Avoidance in Unstructured Dynamic EnvironmentsOpenAlex

Bruno Brito, Boaz Floor, Laura Ferranti, et al.
This letter presents a method for local motion planning in unstructured environments with static and moving obstacles, such as humans. Given a reference path and speed, our optimization-based receding-horizon approach computes a local trajectory that minimizes the tracking error while avoiding obstacles. We build on nonlinear model-predictive contouring control (MPCC) and extend it to incorporate a static map by computing, online, a set of convex regions in free space. We model moving obstacles as ellipsoids and provide a correct bound to approximate the collision region, given by the Minkowsky sum of an ellipse and a circle. Our framework is agnostic to the robot model. We present experimental results with a mobile robot navigating in indoor environments populated with humans. Our method is executed fully onboard without the need of external support and can be applied to other robot morphologies such as autonomous cars.

132Explicitly incorporating surrogate safety measures into connected and automated vehicle longitudinal control objectives for enhancing platoon safety.PubMed

Yulu Dai, Chen Wang, Yuanchang Xie
Accid Anal Prev. 2023 Apr;183:106975. doi: 10.1016/j.aap.2023.106975. Epub 2023 Jan 23.
The concepts of Connected and Automated Vehicles (CAV) and vehicle platooning have generated high expectations regarding the safety performance of future transportation systems. Existing CAV longitudinal control research primarily focuses on efficiency and control stability, by considering different inter-vehicle spacing policies. In very few cases, safety was also considered as a constraint, but not in the main control objectives. Theoretically, stability can only guarantee that CAV platoons eventually achieve an equilibrium state but is unable to promise safety along the process of achieving equilibrium. It is important to note that CAV does not mean absolutely safe, and its longitudinal or platoon control safety performance depends on how the control algorithms are designed, how accurately it can detect and predict its lead vehicle's (could be a human-driven vehicle) next move, and other practical factors such as control and communication delays. To optimize CAV platoon safety, this study integrates surrogate safety measures (SSM) and model predictive control (MPC) into CAV longitudinal control for trajectory optimization. SSM has been widely adopted for modeling the safety consequences of various vehicle control strategies and identifying near-crash events from either simulated or field-captured traffic data. This study directly incorporates three typical SSM into the longitudinal control objectives of CAV and constructs a state-space MPC algorithm to model how these SSM vary as a result of CAV dynamics. Numerical examples are provided to show the performance of these SSM-based optimal CAV longitudinal control methods under traffic flow perturbations. To further confirm the necessity of explicitly considering SSM in CAV longitudinal control and its effectiveness in reducing rear-end collision risk, the proposed methods are compared with three classical longitudinal control models that do not consider SSM based on microscopic traffic simulation. It is noted that all SSM-based optimal control methods perform better than others as manifested by some key risk indicators, demonstrating the importance of explicitly considering SSM and safety in CAV longitudinal control.

133Collision-Free Robot Path Planning by Integrating DRL with Noise Layers and MPC.PubMed

Xinzhan Hong, Qieshi Zhang, Yexing Yang, et al.
Sensors (Basel). 2025 Oct 10;25(20):6263. doi: 10.3390/s25206263.
With the rapid advancement of Autonomous Mobile Robots (AMRs) in industrial automation and intelligent logistics, achieving efficient and safe path planning in dynamic environments has become a critical challenge. These environments require robots to perceive complex scenarios and adapt their motion strategies accordingly, often under real-time constraints. Existing methods frequently struggle to balance efficiency, responsiveness, and safety, especially in the presence of continuously changing dynamic obstacles. While Model Predictive Control (MPC) and Deep Reinforcement Learning (DRL) have each shown promise in this domain, they also face limitations when applied individually-such as high computational demands or insufficient environmental exploration. To address these challenges, we propose a hybrid path planning framework that integrates an optimized DRL algorithm with MPC. We replace the Actor's output with a learnable noisy linear layer whose mean and scale parameters are optimized jointly with the policy via backpropagation, thereby enhancing exploration while preserving training stability. TD3 produces stepwise control commands that evolve into a short-horizon reference trajectory, while MPC refines this trajectory through constraint-aware optimization to ensure timely obstacle avoidance. This complementary process combines TD3's learning-based adaptability with MPC's reliable local feasibility. Extensive experiments conducted in environments with varying obstacle dynamics and densities demonstrate that the proposed method significantly improves obstacle avoidance success rate, trajectory smoothness, and path accuracy compared to traditional MPC, standalone DRL, and other hybrid approaches, offering a robust and efficient solution for autonomous navigation in complex scenarios.

134Infeasibility handling in linear MPC subject to prioritized constraintsOpenAlex

Jostein Vada, Olav Slupphaug, Bjarne Foss

135Efficient infeasibility handling in linear MPC subject to prioritized constraintsOpenAlex

Jostein Vada, Olav Slupphaug, Tor Arne Johansen
All practical MPC implementations should have a means to recover from infeasibility. We propose an algorithm designed for linear state-space MPC which optimally relaxes an infeasible prioritized MPC optimization problem into a feasible one by solving only one LP on-line in addition to the standard MPC optimization problem. By optimal it is meant that the violation of a lower prioritized constraint cannot be made less without increasing the violation of a higher prioritized constraint. It is shown how to design the LP off-line such that the computed constraint violations are optimal.

136Ethical Decision-Making Platform in Autonomous Vehicles With Lexicographic Optimization Based Model Predictive ControllerOpenAlex

Hong Wang, Yanjun Huang, Amir Khajepour, et al.
Ethical decision-making during inevitable crashes, especially when humans involved, has become a big and sensitive roadblock for future mass adoption of autonomous vehicles. Towards addressing this challenge, this paper proposes a predictive control framework for ethical decision-making in autonomous driving using rational ethics. For flexibly implementing of ethical rules, the Lexicographic Optimization-based model predictive controller (LO-MPC) has been designed, in which obstacles and constraints are prioritized. Simulation environment is set up in PreScan, with different edge cases. The results show that the proposed LO-MPC approach has the capability to deal with the ethical decision-making during inevitable crashes by avoiding the obstacles with the assumed priority orders compared with traditional decision-making algorithm.

137Model predictive control of a granulation system using soft output constraints and prioritized control objectivesOpenAlex

Edward P. Gatzke, Francis J. Doyle

138Modeling and model predictive control of a de-manufacturing plantOpenAlex

Andrea Cataldo, Riccardo Scattolini
Dynamic pallet routing optimal control is a crucial task for evolutionary manufacturing plants in order to guarantee efficient production plant performances. In this paper, a new approach based on hybrid Model Predictive Control (MPC) is proposed to control a manufacturing multitarget, multi-pallet transport line. The mathematical representation of the plant is based on a Mixed Linear Dynamical (MLD) model, used by MPC to predict the plant behavior in terms of the future evolution of the state and control variables. The performance index to be minimized is linear and weights the distance of the pallets from their final target. The resulting Mixed Linear Integer Programming (MILP) problem is recursively solved to obtain the control law. Many simulation experiments have been carried out to evaluate the performances of the proposed approach in a realistic scenario. The achieved results confirm the good performances of the control algorithm and its ability to manage even pallet route conflicts and target dynamic re-scheduling.

139Dispatching and conflict-free routing based on model predictive control in semiconductor fabOpenAlex

Ryosuke Nakamura, Kenji Sawada, Seiichi Shin, et al.
This paper proposes a new scheduling method of dispatching and conflict-free routing for overhead hoist transport (OHT) systems in semiconductor fabrication (Fab). This paper utilizes a model predictive control (MPC) strategy in which the cycle of measurement, prediction, optimization and control is repeated. The first aim of the MPC application is to set a small prediction horizon for the scheduling optimization, which leads to reduce computational complexity. The second aim is to address the dynamic situation such that transport requests are given in real time. This paper introduces a switching type multi-objective cost function and considers how the MPC based method adds new request tasks to the scheduling problem in real-time for the dynamic situation. To verify the validity of the proposed method, some numerical examples are shown.

140Courteous MPC for Autonomous Driving with CBF-inspired Risk AssessmentOpenAlex

Yanze Zhang, Yiwei Lyu, Sude E. Demir, et al.
With more autonomous vehicles (AVs) sharing roadways with human-driven vehicles (HVs), ensuring safe and courteous maneuvers that respect HVs' behavior becomes increasingly important. To promote both safety and courtesy in AV's behavior, an extension of Control Barrier Functions (CBFs)-inspired risk evaluation framework is proposed in this paper by considering both noisy observed positions and velocities of surrounding vehicles. The perceived risk by the ego vehicle can be visualized as a risk map that reflects the understanding of the surrounding environment and thus shows the potential for facilitating safe and courteous driving. By incorporating the risk evaluation framework into the Model Predictive Control (MPC) scheme, we propose a Courteous MPC for ego AV to generate courteous behaviors that 1) reduce the overall risk imposed on other vehicles and 2) respect the hard safety constraints and the original objective for efficiency. We demonstrate the performance of the proposed Courteous MPC via theoretical analysis and simulation experiments.

141Merging Control in Mixed Traffic with Safety Guarantees: A Safe Sequencing Policy with Optimal Motion ControlOpenAlex

Ehsan Sabouni, Hussein Ahmad, Christos G. Cassandras, et al.
We address the problem of merging traffic from two roadways consisting of both Connected Autonomous Vehicles (CAVs) and Human Driven Vehicles (HDVs). Guaranteeing safe merging in such mixed traffic settings is challenging due to the unpredictability of possibly uncooperative HDVs. We develop a hierarchical controller where at each discrete time step a coordinator first determines the best possible Safe Sequence (SS) which can be realized without any knowledge of human driving behavior. Then, a lower-level decentralized motion controller for each CAV jointly minimizes travel time and energy over a prediction horizon, subject to hard safety constraints dependent on the given safe sequence. This is accomplished using a Model Predictive Controller (MPC) subject to constraints based on Control Barrier Functions (CBFs) which render it computationally efficient. Extensive simulation results are included showing that this hierarchical controller outperforms the commonly adopted Shortest Distance First (SDF) passing sequence over the full range of CAV penetration rates, while also providing safe merging guarantees.

142LanguageMPC: Large Language Models as Decision Makers for Autonomous DrivingOpenAlex

Hao Sha, Yao Mu, Yuxuan Jiang, et al.
Existing learning-based autonomous driving (AD) systems face challenges in comprehending high-level information, generalizing to rare events, and providing interpretability. To address these problems, this work employs Large Language Models (LLMs) as a decision-making component for complex AD scenarios that require human commonsense understanding. We devise cognitive pathways to enable comprehensive reasoning with LLMs, and develop algorithms for translating LLM decisions into actionable driving commands. Through this approach, LLM decisions are seamlessly integrated with low-level controllers by guided parameter matrix adaptation. Extensive experiments demonstrate that our proposed method not only consistently surpasses baseline approaches in single-vehicle tasks, but also helps handle complex driving behaviors even multi-vehicle coordination, thanks to the commonsense reasoning capabilities of LLMs. This paper presents an initial step toward leveraging LLMs as effective decision-makers for intricate AD scenarios in terms of safety, efficiency, generalizability, and interoperability. We aspire for it to serve as inspiration for future research in this field. Project page: https://sites.google.com/view/llm-mpc

143A MPC Combined Decision Making and Trajectory Planning for Autonomous Vehicle Collision AvoidanceOpenAlex

Manel Ammour, Rodolfo Orjuela, Michel Basset
Increasing focus is being paid to ensuring safety in autonomous driving. The current paper addresses the challenge of collision avoidance with dynamic surrounding vehicles in different driving situations. The established solution formulated utilizing Model Predictive Control (MPC) includes decision making and trajectory planning. A simplified prediction model is used, which takes into account the relative positions and velocities of the surrounding vehicles and the ego vehicle. Depending on traffic conditions, which are stated as constraints in the MPC formulation, the ego vehicle may perform lane keeping, lane shift, overtaking or braking to avoid collision with the road participants. The decision making constraints are included into the MPC in a mixed integer formulation-like manner. The safety constraints are defined using the Sigmoid function and the braking barrier to define the navigable zone of the ego vehicle. The proposed algorithm has been evaluated through simulation, with different scenarios revealing its effectiveness.

144A Practical MPC Method for Autonomous Driving Longitudinal Dynamic Control's Real-World ChallengesOpenAlex

Junbo Jing, Jingxuan Liu, Chunan Huang, et al.
Autonomous driving's Planning-and-Control (PnC) integration demands alignment in vehicle motion feasibility and motion error predictability, which requires the motion controller to respect realistic vehicle system constraints and dynamic properties. This paper describes a Model Predictive Control (MPC) method that practically handles the system challenges in vehicle longitudinal dynamic control, introduced by complex torque capacity shapes, system switching by gear shifts, and multiple actuation systems. Techniques of constraint local affine approximation, wheel and actuator domain separation, and fuel mapping blending are invented to address the aforementioned challenges, leading to quasi-optimal control solution using minimal computation time. Through formulating the control problem into constrained multi-objective optimizations, product & functional requirements involved in autonomous driving, such as tracking response, safety constraints, fuel economy, ride comfort, are conveniently handled and explicitly satisfied over a wide range of scenarios using a single control core solver. This controller has been sufficiently validated and supports TuSimple's class-8 truck autonomous driving operations in real traffic of Arizona and Texas in USA.

145Approximate hybrid model predictive control for multi-contact push recovery in complex environmentsOpenAlex

Tobia Marcucci, Robin Deits, Marco Gabiccini, et al.
Feedback control of robotic systems interacting with the environment through contacts is a central topic in legged robotics. One of the main challenges posed by this problem is the choice of a model sufficiently complex to capture the discontinuous nature of the dynamics but simple enough to allow online computations. Linear models have proved to be the most effective and reliable choice for smooth systems; we believe that piecewise affine (PWA) models represent their natural extension when contact phenomena occur. Discrete-time PWA systems have been deeply analyzed in the field of hybrid Model Predictive Control (MPC), but the straightforward application of MPC techniques to complex systems, such as a humanoid robot, leads to mixed-integer optimization problems which are not solvable at real-time rates. Explicit MPC methods can construct the entire control policy offline, but the resulting policy becomes too complex to compute for systems at the scale of a humanoid robot. In this paper we propose a novel algorithm which splits the computational burden between an offline sampling phase and a limited number of online convex optimizations, enabling the application of hybrid predictive controllers to higher-dimensional systems. In doing so we are willing to partially sacrifice feedback optimality, but we set stability of the system as an inviolable requirement. Simulation results of a simple planar humanoid that balances by making contact with its environment are presented to validate the proposed controller.

146Data-Driven Control of Soft Robots Using Koopman Operator TheoryOpenAlex

Daniel Bruder, Xun Fu, R. Brent Gillespie, et al.
Controlling soft robots with precision is a challenge due to the difficulty of constructing models that are amenable to model-based control design techniques. Koopman operator theory offers a way to construct explicit dynamical models of soft robots and to control them using established model-based control methods. This approach is data driven, yet yields an explicit control-oriented model rather than just a “black-box” input-output mapping. This work describes a Koopman-based system identification method and its application to model predictive control (MPC) design for soft robots. Three MPC controllers are developed for a pneumatic soft robot arm via the Koopman-based approach, and their performances are evaluated with respect to several real-world trajectory following tasks. In terms of average tracking error, these Koopman-based controllers are more than three times more accurate than a benchmark MPC controller based on a linear state-space model of the same system, demonstrating the utility of the Koopman approach in controlling real soft robots.

147Context-aware robotic arm using fast embedded model predictive controlOpenAlex

Shane Trimble, Wasif Naeem, Seán McLoone, et al.
The growing number of collaborative robotics in unstructured environments creates highly nonconvex nonlinear shared dynamical systems. For safety and speed, path planning and collision avoidance are of the utmost importance in these situations. We present a novel nonlinear MPC solution for use on a three-dimensional four-axis robotic manipulator. The system is the first of it's kind to take into account moving obstacles. Using the OpEn framework, optimisation is done by the PANOC and ALM techniques. Experimentation demonstrates extremely fast solver times on both PC and embedded platforms.

148A hybrid obstacle avoidance method for mobile robot navigation in unstructured environmentOpenAlex

Huaidong Zhou, Pengbo Feng, Wusheng Chou
Purpose Wheeled mobile robots (WMR) are the most widely used robots. Avoiding obstacles in unstructured environments, especially dynamic obstacles such as pedestrians, is a serious challenge for WMR. This paper aims to present a hybrid obstacle avoidance method that combines an informed-rapidly exploring random tree* algorithm with a three-dimensional (3D)-object detection approach and model prediction controller (MPC) to conduct obstacle perception, collision-free path planning and obstacle avoidance for WMR in unstructured environments. Design/methodology/approach Given a reference orientation and speed, the hybrid method uses parametric ellipses to represent obstacle expansion boundaries based on the 3D target detection results, and a collision-free reference path is planned. Then, the authors build on a model predictive control for tracking the collision-free reference path by incorporating the distance between the robot and obstacles. The proposed framework is a mapless method for WMR. Findings The authors present experimental results with a mobile robot for obstacle avoidance in indoor environments crowded with obstacles, such as chairs and pedestrians. The results show that the proposed hybrid obstacle avoidance method can satisfy the application requirements of mobile robots in unstructured environments. Originality/value In this study, the parameter ellipse is used to represent the area occupied by the obstacle, which takes the velocity as the parameter. Therefore, the motion direction and position of dynamic obstacles can be considered in the planning stage, which enhances the success rate of obstacle avoidance. In addition, the distance between the obstacle and robot is increased in the MPC optimization function to ensure a safe distance between the robot and the obstacle.

149A Review on Federated Learning Architectures for Privacy-Preserving AI: Lightweight and Secure Cloud–Edge–End CollaborationOpenAlex

Shanhao Zhan, Lianfen Huang, Gaoyu Luo, et al.
Federated learning (FL) has emerged as a promising paradigm for enabling collaborative training of machine learning models while preserving data privacy. However, the massive heterogeneity of data and devices, communication constraints, and security threats pose significant challenges to its practical implementation. This paper provides a system review of the state-of-the-art techniques and future research directions in FL, with a focus on addressing these challenges in resource-constrained environments by a cloud–edge–end collaboration FL architecture. We first introduce the foundations of cloud–edge–end collaboration and FL. We then discuss the key technical challenges. Next, we delve into the pillars of trustworthy AI in the federated context, covering robustness, fairness, and explainability. We propose a dimension reconstruction of trusted AI and analyze the foundations of each trustworthiness pillar. Furthermore, we present a lightweight FL framework for resource-constrained edge–end devices, analyzing the core contradictions and proposing optimization paradigms. Finally, we highlight advanced topics and future research directions to provide valuable insights into the field.

150Privacy-Preserving Federated Learning for Space–Air–Ground Integrated Networks: A Bi-Level Reinforcement Learning and Adaptive Transfer Learning Optimization FrameworkOpenAlex

Ling Li, Lidong Zhu, Weibang Li
The Space-Air-Ground Integrated Network (SAGIN) has emerged as a core architecture for future intelligent communication due to its wide-area coverage and dynamic heterogeneous characteristics. However, its high latency, dynamic topology, and privacy-security challenges severely constrain the application of Federated Learning (FL). This paper proposes a Privacy-Preserving Federated Learning framework for SAGIN (PPFL-SAGIN), which for the first time integrates differential privacy, adaptive transfer learning, and bi-level reinforcement learning to systematically address data heterogeneity, device dynamics, and privacy leakage in SAGINs. Specifically, (1) an adaptive knowledge-sharing mechanism based on transfer learning is designed to balance device heterogeneity and data distribution divergence through dynamic weighting factors; (2) a bi-level reinforcement learning device selection strategy is proposed, combining meta-learning and hierarchical attention mechanisms to optimize global-local decision-making and enhance model convergence efficiency; (3) dynamic privacy budget allocation and robust aggregation algorithms are introduced to reduce communication overhead while ensuring privacy. Finally, experimental evaluations validate the proposed method. Results demonstrate that PPFL-SAGIN significantly outperforms baseline solutions such as FedAvg, FedAsync, and FedAsyncISL in terms of model accuracy, convergence speed, and privacy protection strength, verifying its effectiveness in addressing privacy preservation, device selection, and global aggregation in SAGINs.

151SecFedDNN: A Secure Federated Deep Learning Framework for Edge–Cloud EnvironmentsOpenAlex

Roba H. Alamir, Ayman Noor, Hanan Almukhalfi, et al.
Cyber threats that target Internet of Things (IoT) and edge computing environments are growing in scale and complexity, which necessitates the development of security solutions that are both robust and scalable while also protecting privacy. Edge scenarios require new intrusion detection solutions because traditional centralized intrusion detection systems (IDSs) lack in the protection of data privacy, create excessive communication overhead, and show limited contextual adaptation capabilities. This paper introduces the SecFedDNN framework, which combines federated deep learning (FDL) capabilities to protect edge–cloud environments from cyberattacks such as Distributed Denial of Service (DDoS), Denial of Service (DoS), and injection attacks. SecFedDNN performs edge-level pre-aggregation filtering through Layer-Adaptive Sparsified Model Aggregation (LASA) for anomaly detection while supporting balanced multi-class evaluation across federated clients. A Deep Neural Network (DNN) forms the main model that trains concurrently with multiple clients through the Federated Averaging (FedAvg) protocol while keeping raw data local. We utilized Google Cloud Platform (GCP) along with Google Colaboratory (Colab) to create five federated clients for simulating attacks on the TON_IoT dataset, which we balanced across selected attack types. Initial tests showed DNN outperformed Long Short-Term Memory (LSTM) and SimpleNN in centralized environments by providing higher accuracy at lower computational costs. Following federated training, the SecFedDNN framework achieved an average accuracy and precision above 84% and recall and F1-score above 82% across all clients with suitable response times for real-time deployment. The study proves that FDL can strengthen intrusion detection across distributed edge networks without compromising data privacy guarantees.

152Online Trajectory Generation With Distributed Model Predictive Control for Multi-Robot Motion PlanningOpenAlex

Carlos E. Luis, Marijan Vukosavljev, Angela P. Schoellig
We present a distributed model predictive control (DMPC) algorithm to generate trajectories in real-time for multiple robots. We adopted the on-demand collision avoidance method presented in previous work to efficiently compute non-colliding trajectories in transition tasks. An event-triggered replanning strategy is proposed to account for disturbances. Our simulation results show that the proposed collision avoidance method can reduce, on average, around 50% of the travel time required to complete a multi-agent point-to-point transition when compared to the well-studied Buffered Voronoi Cells (BVC) approach. Additionally, it shows a higher success rate in transition tasks with a high density of agents, with more than 90% success rate with 30 palm-sized quadrotor agents in a 18 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> arena. The approach was experimentally validated with a swarm of up to 20 drones flying in close proximity.