Taherian Shayan, Halder Kaushik, Dixit Shilp, Fallah Saber
Department of Mechanical Engineering Sciences, Connected Autonomous Vehicle Lab (CAV-Lab), University of Surrey, Guildford GU2 7XH, UK.
Sensors (Basel). 2021 Jun 23;21(13):4296. doi: 10.3390/s21134296.
Model predictive control (MPC) is a multi-objective control technique that can handle system constraints. However, the performance of an MPC controller highly relies on a proper prioritization weight for each objective, which highlights the need for a precise weight tuning technique. In this paper, we propose an analytical tuning technique by matching the MPC controller performance with the performance of a linear quadratic regulator (LQR) controller. The proposed methodology derives the transformation of a LQR weighting matrix with a fixed weighting factor using a discrete algebraic Riccati equation (DARE) and designs an MPC controller using the idea of a discrete time linear quadratic tracking problem (LQT) in the presence of constraints. The proposed methodology ensures optimal performance between unconstrained MPC and LQR controllers and provides a sub-optimal solution while the constraints are active during transient operations. The resulting MPC behaves as the discrete time LQR by selecting an appropriate weighting matrix in the MPC control problem and ensures the asymptotic stability of the system. In this paper, the effectiveness of the proposed technique is investigated in the application of a novel vehicle collision avoidance system that is designed in the form of linear inequality constraints within MPC. The simulation results confirm the potency of the proposed MPC control technique in performing a safe, feasible and collision-free path while respecting the inputs, states and collision avoidance constraints.
模型预测控制（MPC）是一种能够处理系统约束的多目标控制技术。然而，MPC控制器的性能高度依赖于每个目标的适当优先级权重，这凸显了精确权重调整技术的必要性。在本文中，我们提出了一种通过将MPC控制器性能与线性二次调节器（LQR）控制器性能相匹配的解析调整技术。所提出的方法使用离散代数黎卡提方程（DARE）推导出具有固定加权因子的LQR加权矩阵的变换，并在存在约束的情况下利用离散时间线性二次跟踪问题（LQT）的思想设计MPC控制器。所提出的方法确保了无约束MPC和LQR控制器之间的最优性能，并在瞬态操作期间约束激活时提供次优解决方案。通过在MPC控制问题中选择合适的加权矩阵，所得的MPC表现为离散时间LQR，并确保系统的渐近稳定性。在本文中，在所提出的技术应用于以MPC内的线性不等式约束形式设计的新型车辆碰撞避免系统中研究了其有效性。仿真结果证实了所提出的MPC控制技术在尊重输入、状态和碰撞避免约束的同时执行安全、可行且无碰撞路径方面的效力。
