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  

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

作　　者：李丽 卢延荣[3] 于晓 LI Li;LU Yan-rong;YU Xiao(School of Information Management and Statistics,Hubei University of Economics,Wuhan 430205,China;Hubei Center for Data and Analysis,Hubei University of Economics,Wuhan 430205,China;School of Mathematics and Physics,University of Science and Technology Beijing,Beijing 100083,China;School of Science,Shangdong Jianzhu University,Jinan 250101,China)

机构地区：[1]湖北经济学院信息管理与统计学院,武汉430205 [2]湖北经济学院湖北数据与分析中心,武汉430205 [3]北京科技大学数理学院,北京100083 [4]山东建筑大学理学院,济南250101

出　　处：《控制与决策》2021年第9期2074-2084,共11页Control and Decision

基　　金：国家自然科学基金项目(61903130);湖北省自然科学基金项目(2019CFB227)。

摘　　要：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.Based on the parameter-dependent Lyapunov function method and the LMI technique,the problem of finitetime 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 finitetime 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.

关 键 词：扩大误差系统 预见控制 参数不确定系统 有限时间稳定 输出反馈 鲁棒跟踪 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]