含状态和输入时滞离散时间系统近似最优跟踪控制.PDF

第32 卷 第1 期 控 制 与 决 策 Vol. 32 No. 1 2017 年 1 月 Control and Decision Jan. 2017 文章编号: 1001-0920 (2017) 01-0157-06 DOI: 10.13195/j.kzyjc.2016.0060 含状态和输入时滞的离散时间系统的近似最优跟踪控制 张 健, 宿 浩 , 王鲁昆, 唐功友 ( 中国海洋大学信息科学与工程学院，山东青岛266100) 摘 要: 针对状态和控制输入均含有时滞的离散时间系统, 提出最优跟踪控制的设计方法. 通过引入一种新的状态 向量, 将含有状态和控制输入时滞的离散时间系统转化为含有虚拟扰动项的无时滞离散时间系统. 根据最优控制理 论, 构造离散Riccati 矩阵方程和离散Stein 矩阵方程的序列, 并证明该解序列一致收敛于变换后的离散时间系统的最 优跟踪控制策略. 利用最优控制的逐次逼近设计方法, 得到最优跟踪控制的近似解, 并给出求解最优跟踪控制律的算 法. 仿真算例表明了所提出最优跟踪控制方法的有效性. 关键词: 时滞系统；离散时间系统；最优控制；最优输出跟踪；逐次逼近法 中图分类号: TP273 文献标志码: A Optimal output tracking control for discrete-time systems with delayed state and input ZHANG Jian, SU Hao , WANG Lu-kun, TANG Gong-you (College of Information Science and Engineering，Ocean University of China，Qingdao 266100，China) Abstract: This paper proposes a design method of optimal tracking control for discrete-time systems with the delayed state and input. By introducing a new state vector, the original system is transformed into a non-delay discrete-time system with virtual disturbance. According to the optimal control theory, a sequence of discrete Riccati matrix equations and Stein matrix difference equations are constructed, and the solution sequence is proved to converge to the optimal tracking strategy of the transformed discrete-time system. By using the successive approximation design method of optimal control, the approximate solution of the optimal tracking control is obtained, and a design algorithm of the optimal tracking control law is presented. Simulation examples are given to illustrate the effectiveness of the proposed approach. Ke