一类Lipschitz非线性离散系统的可靠预见跟踪控制  

Reliable Preview Tracking Control for a Class of Discrete-Time Lipschitz Nonlinear Systems

作　　者：于晓 鲁润翰 袁远龙 YU Xiao;LU Runhan;YUAN Yuanong(School of Science,Shandong Jianzhu University,Jinan 250101;School of Computer and Information Engineering,Jiangri Agricultural University,Nanchang 330045)

机构地区：[1]山东建筑大学理学院,济南250101 [2]江西农业大学计算机与信息工程学院,南昌330045

出　　处：《系统科学与数学》2023年第11期2804-2819,共16页Journal of Systems Science and Mathematical Sciences

基　　金：山东省自然科学基金(ZR2020QA036);山东省高校青创科技计划(2021K J067);山东建筑大学博研基金(X19053Z)资助课题。

摘　　要：针对一类含执行器故障的离散时间Lipschitz非线性系统,提出基于线性矩阵不等式(LMI)的可靠预见跟踪控制器设计方法.首先,采用差分方法以及状态增广技术,并且融合参考信号和干扰的预见信息,构造扩大误差系统,将可靠预见跟踪控制问题转化为可靠镇定问题.其中,微分中值定理的使用克服了非线性函数差分处理上的困难,使得扩大误差系统是一个形式上的线性参变系统.然后,提出静态输出反馈可靠控制器,并且以LMI的形式给出保证闭环系统渐近稳定的充分条件.基于此,给出原系统的可靠预见控制器,使得闭环系统实现对目标信号的渐近跟踪.最后,通过一个数值例子验证所提设计方法的有效性.For a class of discrete-time Lipschitz nonlinear systems with actuator faults,a reliable preview tracking controller design method based on linear matrix inequality(LMI)is proposed.Firstly,with the aid of the difference method and the state augmentation technique,and fusing the preview information of reference signal and disturbance,an augmented error system is constructed,which transforms the reliable preview tracking control problem into a reliable stabilization problem.The use of the differential mean value theorem overcomes the difficulty of dealing with the difference of nonlinear functions,making the augmented error system be a formal linear parameter varying system.Then,a static output feedback reliable controller is proposed,and a sufficient condition for the asymptotic stability of the closed-loop system is given in the form of LMI.Based on this,the reliable preview controller of the original system is obtained.Finally,a numerical example is given to verify the effectiveness of the proposed design method.

关 键 词：LIPSCHITZ非线性系统 预见控制 可靠控制 执行器故障 输出反馈 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]