时变参数不确定广义系统的有限时间预见控制器设计  

Design of Finite-time Preview Controller for Time-varying Parameter Uncertain Descriptor Systems

作　　者：李丽[1,2] 卢延荣 LI Li;LU Yanrong(School of Statistics and Mathematics,Hubei University of Economics,Wuhan 430205,China;Hubei Center for Data and Analysis,Wuhan 430205,China;College of Electrical and Information Engineering,Lanzhou University of Technology,Lanzhou 73050,China)

机构地区：[1]湖北经济学院统计与数学学院,武汉430205 [2]湖北经济学院湖北数据与分析中心,武汉430205 [3]兰州理工大学电气与信息工程学院,730050

出　　处：《应用数学学报》2022年第5期712-731,共20页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(61903130);山东省自然科学基金(ZR2020QA036);湖北省教育厅科研重点(D20192202);湖北经济学院科研培育(PYYB202007,PYZD202005)资助项目。

摘　　要：基于具有参数依赖的Lyapunov函数方法及LMI技巧,本文研究一类具有时变参数不确定广义离散时间系统的有限时间预见控制问题.首先,采用预见控制理论中误差系统的方法,引入两个辅助变量和离散提升技术,构造出包含未来目标值信号的信息的扩大误差系统,将有限时间预见跟踪问题转化为扩大误差系统的有限时间稳定性问题;然后,针对所推导的扩大误差系统,考虑输出反馈时,改造输出方程,使其包含可预见信号的信息,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.通过求解LMI,即可确定预见控制器增益矩阵.数值仿真表明本文结果的有效性.Based on parameter-dependent Lyapunov function method with the LMI technique,the problem of finite-time preview control is proposed for uncertain descriptor systems with time-varying parameters.First an augmented error system including previewed information is constructed by using the error system method of preview control theory and introducing two auxiliary variables and discrete lifting technique.And the finite time preview tracking control problem is transformed into a finite time stability of augmented error systems.Then,while considering the output feedback,a previewable reference signal is fully utilized through reformulation of the output equation for the derived augmented error system.The conditions are derived for the finite-time stability of the closed-loop systems and design of preview controller is proposed.The gains of preview controller can be realized by solving an LMI problem.The numerical simulation examples also illustrate the effectiveness of the results in the paper.

关 键 词：扩大误差系统 预见控制 跟踪控制 不确定广义系统 时变参数 有限时间稳定 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]