参数不确定离散时间系统的有限时间输出反馈预见控制器设计

基于参数依赖的Lyapunov函数方法及LMI技巧,研究一类参数不确定离散时间系统的有限时间输出反馈预见控制问题.首先,采用预见控制理论中误差系统的方法,引入差分算子和离散提升技术,构造出包含未来目标值信号和干扰信号的信息的扩大误差系统,将有限时间预见控制问题转化为扩大误差系统的有限时间稳定性问题;然后,针对所推导出的扩大误差系统设计输出反馈预见控制器,通过改造输出方程以充分利用可预见信号的未来信息,并通过LMI技巧给出闭环系统有限时间稳定的条件及预见控制器的设计方法.研究结果表明,通过求解LMI,可确定静态输出反馈预见控制器增益矩阵.数值仿真表明了所提出方法的有效性.

Design of finite-time output feedback preview controller for discrete-time systems with parameter uncertainty

Based on the parameter-dependent Lyapunov function method and the LMI technique, the problem of finite-time output feedback preview control is proposed for a class of polytopic uncertain discrete-time systems. Firstly, the difference operator is introduced, the discrete lifting technology is employed, and an augmented error system including previewed information is constructed by using the error system method in preview control theory, which leads to a finite-time preview control problem being transformed into a finite time stabilization problem. Then, the previewable signals are fully utilized through reformulation of the output equation, considering the output feedback for the augmented error system, the condition of finite-time stability of closed-loop system and the design method of preview controller are given by LMI technique. Research result shows that the static output preview controller parameter matrices can be achieved from the solution of LMIs problems. The numerical simulation examples illustrate the validity of the proposed method in this paper.