不确定离散时间输入饱和系统的鲁棒预见控制

Robust Preview Control for Uncertain Discrete-time Systems with Actuator Saturation

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.

This paper investigates the problem of robust preview control for uncertain discrete-time systems with actuator saturation.Different from the previous difference between error signal and system equation,the auxiliary variable related to the system state is introduced.The difference between the system state vector and the corresponding auxiliary variable is used to replace the usual state difference,which makes it possible to construct the augmented error system of uncertain discrete system with input saturation.In addition,the error vector is not added to the augmented error system as usual,which not only reduces the order of the system but also allows the output matrix to have uncertainties.For the augmented error system,the state feedback and static output feedback are both considered and the sufficient conditions for the closed-loop system to be asymptotically stable are derived by using Lyapunov function and LMI technique.The numerical simulation shows the validity of the results in the paper.