输入饱和时变参数不确定离散时间系统的预见控制

Preview Control for Discrete-Time Polytopic Time-Varying Systems with Input Saturation

针对一类时变参数饱和离散时间系统,为了实现系统预见跟踪性能,文章提出了一种目标值信号预见补偿控制方法.首先,引入一个与状态变量有关的辅助变量,构造出包含目标值信号未来信息的扩大误差系统,将原系统的预见跟踪问题转化为扩大误差系统的H控制问题;然后,针对所推导的扩大误差系统,采用一种改进后的扇形条件处理饱和项,并提出一个带有预见作用的状态反馈.基于Lyapunov稳定性理论和线性矩阵不等式(LMI)技巧,给出闭环系统渐近稳定的充分条件及预见控制器的设计方法.通过求解LMI,确定预见控制器增益矩阵.数值仿真表明文章结果的有效性.

For a class of uncertain discrete-time systems with time-varying polytopic and input saturation,a control method of reference preview compensation is proposed to achieve preview tracking performance in this paper.First,an auxiliary variable related to the state variable is introduced to constructed the augmented error system including previewed information.This leads to the preview control problem of the original system is transformed into the Hcontrol problem of the augmented error system.Then,for the augmented error system,a sector condition handles saturation is proposed to deal with the input saturation and a state feedback with preview actions is presented.Based on Lyapunov method and LMI technique,the conditions of asymptotic stability of the closed-loop system and the design method of the preview controller are given.The preview controller’s gain matrix is obtained by solving LMI.Finally,the effectiveness of the results in this paper is illustrated by numerical simulation examples.