不确定离散时间输入饱和系统的鲁棒预见控制

This paper studies the robust preview control problem of a class of uncertain discrete-time systems with input saturation. Different from taking differences of error signals and system equations in the past, this paper introduces state auxiliary variables and uses the difference between the system state vector and the auxiliary variables to replace the usual state difference, making it possible to construct the augmented error system of the input-saturated uncertain discrete system. In addition, the augmented error system derived in this paper no longer contains the error vector, which not only reduces the order of the system but also allows the output matrix to have uncertain terms. For the augmented error system, state feedback and static output feedback are introduced respectively, and by using Lyapunov function and LMI techniques, sufficient conditions for the asymptotic stability of the closed-loop system are derived. Numerical simulations demonstrate the effectiveness of the results in this paper.

本文研究一类具有输入饱和的不确定离散时间系统的鲁棒预见控制问题.与以往对误差信号和系统方程取差分不同,本文引入状态辅助变量,利用系统状态向量与辅助变量之差代替通常的状态差分,使得输入饱和不确定离散系统的扩大误差系统的构造成为可能.另外,本文推导的扩大误差系统不再包含误差向量,这不仅降低系统的阶数而且允许输出矩阵带有不确定项.针对扩大误差系统,分别引入状态反馈和静态输出反馈,并利用Lyapunov函数及LMI技巧,导出闭环系统渐近稳定的充分条件.数值仿真表明了本文结果的有效性.