Dai Li, Qiang Zhiwen, Sun Zhongqi, Zhou Tianyi, Xia Yuanqing
IEEE Trans Cybern. 2022 Jun;52(6):5301-5310. doi: 10.1109/TCYB.2020.3030021. Epub 2022 Jun 16.
In this article, we propose a novel economic model-predictive control (MPC) algorithm for a group of disturbed linear systems and implement it in a distributed manner. The system consists of multiple subsystems interacting with each other via dynamics and aims to optimize an economic objective. Each subsystem is subject to constraints both on states and inputs as well as unknown but bounded disturbances. First, we divide the computation of control inputs into several local optimization problems based on each subsystem's local information. This is done by introducing compatibility constraints to confine the difference between the actual information and the previously published reference information of each subsystem, which is the key feature of the proposed distributed algorithm. Then, to ensure the satisfaction of both state and input constraints under disturbances, constraints are tightened on the state and the input of nominal systems by considering explicitly the effect of uncertainties. Moreover, based on an overall optimal steady state, a dissipativity constraint and a terminal constraint are designed and incorporated in the local optimization problems to establish recursive feasibility and guarantee stability for the resulting closed-loop system. Finally, the efficiency of the distributed economic MPC algorithm is demonstrated in a building temperature control case study.
在本文中，我们针对一组受干扰的线性系统提出了一种新颖的经济模型预测控制（MPC）算法，并以分布式方式实现该算法。该系统由多个通过动力学相互作用的子系统组成，旨在优化一个经济目标。每个子系统都受到状态和输入的约束以及未知但有界的干扰。首先，我们基于每个子系统的局部信息将控制输入的计算划分为几个局部优化问题。这是通过引入兼容性约束来限制每个子系统的实际信息与先前发布的参考信息之间的差异来实现的，这是所提出的分布式算法的关键特征。然后，为了确保在干扰下状态和输入约束都能得到满足，通过明确考虑不确定性的影响，对标称系统的状态和输入收紧约束。此外，基于一个全局最优稳态，设计了一个耗散性约束和一个终端约束，并将其纳入局部优化问题中，以建立递归可行性并保证所得闭环系统的稳定性。最后，在一个建筑温度控制案例研究中展示了分布式经济MPC算法的效率。
