不确定输入饱和系统的有限时间预见控制

Finite-Time Preview Control for Uncertain Systems with Input Saturation

文章研究了一类不确定输入饱和系统的有限时间预见控制问题.为避免对时变的系数矩阵和饱和非线性项取差分,文章使用系统状态与状态辅助变量之差代替通常的状态差分,构造了一种新的形式“扩大误差系统”,从而将有限时间预见饱和控制问题转化为扩大误差系统的有限时间稳定性问题.该扩大误差系统不包含误差向量,不仅降低了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,文章引入反馈控制,并利用改进的扇形条件及LMI (linear matrix inequality)技巧,导出了闭环系统有限时间稳定的充分条件及预见饱和控制器的设计方法.数值仿真表明了文章结果的有效性.

In this paper,the finite-time preview control problem for a class of uncertain saturated systems is studied.In order to avoid the difference between the time-varying coefficient matrix and the saturated nonlinear term,this paper utilizes the difference between the system state variables and the corresponding auxiliary variables,instead of the usual difference between system states,and constructs a new form of "augmented error system",which converts the finite-time preview saturated control problem into the finite-time stabilization problem of the augmented error system.The augmented error system no longer contains error vector,which not only reduces the order of the system,but also allows the output matrix to contain uncertainties.For the augmented error system,the feedback control is introduced,and the sufficient conditions for the finite-time stability of the closed-loop system and the design method of the predictive saturated controller are derived by using the improved sector condition and LMI(Linear Matrix Inequality).The numerical simulation examples also illustrate the effectiveness of the results in the paper.