针对一类具有参数不确定性的线性系统, 基于连续/离散二维混合模型进行改进型重复控制系统的保性能设计. 首先给出一种具有反馈作用的改进型重复控制系统结构, 通过独立地考虑重复控制系统的连续控制行为与离散学习行为, 建立重复控制系统的连续/离散二维混合模型, 并将重复控制的设计问题转化为一类连续/离散二维系统的状态反馈控制问题. 然后, 应用二维Lyapunov泛函导出保性能改进型重复控制器存在的充分条件, 进而证明该条件等价于一个线性矩阵不等式可解性问题. 最后通过求解对应的凸优化问题, 给出了最优保性能控制器的具体形式. 数值仿真验证了所提出方法的有效性.
This paper deals with the problem of designing a guaranteed cost modified repetitive control system based on two dimensional (2D) hybrid model for a class of linear systems with parametric uncertainties. First, by analyzing of the continuous control process and discrete learning process independently, the structure of a feedback modified repetitive control (FMRC) system is given and a hybrid continuous-discrete 2D model for the FMRC system is established. Then, the FMRC design problem is converted to the design problem of the continuous-discrete 2D systems with a state feedback. Next, by using the 2D Lyapunov theory, a sufficient condition for existence of guaranteed cost modified repetitive control is obtained. Furthermore, it is pointed out that the condition is equivalent to the solvability problem of a linear matrix inequality. Finally, the design problem of the optimal guaranteed cost control is formulated in solution of the associated convex optimization problem. The validity of the method is verified by a numerical example.