数据驱动的未知线性离散系统双模模型预测控制  

Data-driven dual-mode model predictive control for unknown linear discrete systems

作　　者：刘鑫[1,2] 严爱军[1,2,3] LIU Xin;YAN Ai-jun(School of Information Science and Technology,Beijing University of Technology,Beijing 100124,China;Engineering Research Center of Digital Community of Ministry of Education,Beijing 100124,China;Beijing Laboratory for Urban Mass Transit,Beijing 100124,China)

机构地区：[1]北京工业大学信息科学技术学院,北京100124 [2]数字社区教育部工程研究中心,北京100124 [3]城市轨道交通北京实验室,北京100124

出　　处：《控制与决策》2025年第3期813-821,共9页Control and Decision

基　　金：国家自然科学基金项目(62373017,62073006);北京市自然科学基金项目(4212032).

摘　　要：针对模型参数未知的线性离散系统,提出一种数据驱动的双模模型预测控制方法,无需预先对系统进行建模,能够实现在约束条件下对目标设定点的最优跟踪控制.首先,根据有限的系统历史运行数据预测系统未来一段时间的运行轨迹,并在代价函数中加入实时优化的人工平衡点,通过在线求解滚动优化问题来获得控制输入,进而平稳地驱动系统进入一个控制不变集内;然后,在控制不变集内,基于系统历史运行数据,采用策略迭代的方法求解动态反馈控制器,同时可得到静态前馈控制器,实现驱动系统收敛至平衡点的局部最优跟踪控制;最后,验证所提出方法的稳定性,并将其应用于一个线性化的四容水箱系统.实验结果表明,所提出方法有效可行,具有更小的超调量和更好的收敛性能.This paper proposes a data-driven dual-mode model predictive control method for linear discrete systems with unknown parameters,eliminating the need for system modeling.The proposed method enables optimal tracking of the setpoint under constraints.First,the system's future trajectory is predicted based on limited historical operational data,and a real-time optimized artificial equilibrium point is incorporated into the cost function.Control inputs are then determined by solving an online rolling optimization problem,driving the system into a control-invariant set.Within this invariant set,a dynamic feedback controller is derived using the policy iteration method based on historical operational data,and a static feedforward controller is also obtained,achieving locally optimal control in guiding the system to converge to the equilibrium point.Finally,the stability of the proposed method is proven,and it is applied to a linearized four-tank system.Experimental results demonstrate the effectiveness and feasibility of the proposed method,with reduced overshoot and improved convergence performance.

关 键 词：模型预测控制 线性离散系统 约束系统 数据驱动 最优控制 稳定性分析 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]