饱和时滞非线性系统的间接线性矩阵不等式抗饱和设计  

Anti-windup design for saturated time-delay nonlinear systems:an indirect linear matrix inequality-based approach

作　　者：李豪杰 何汉林[1] 查苗 LI Hao-jie;HE Han-lin;ZHA Miao(Department of Basic Courses,Naval University of Engineering,Wuhan Hubei 430032,China)

机构地区：[1]海军工程大学基础部,湖北武汉430032

出　　处：《控制理论与应用》2020年第7期1595-1600,共6页Control Theory & Applications

基　　金：国家自然科学基金项目(61374003);海军工程大学基础研究基金项目(20161475)资助。

摘　　要：当时滞非线性系统具有执行器饱和时,其稳定性无法得到保证.为了寻找饱和时滞非线性系统的稳定控制器,本文阐述了一种间接线性矩阵不等式(LMI)一步抗饱和设计方法.首先,利用Takagi-Sugeno(T-S)模糊模型将一类饱和时滞非线性系统精确重构,引入输出反馈并行分布补偿系统得到闭环控制系统.然后,运用李雅普诺夫稳定性理论,导出闭环系统的稳定条件,利用一个矩阵不等式的等价引理,将闭环系统稳定条件间接的转化为两个LMIs条件,进而得到间接LMI抗饱和补偿算法,同时给出了吸引域估计及其优化模型.最后给出了应用此方案的一个仿真实例.The stability of time-delay nonlinear systems cannot be guaranteed when it has actuator saturation.Motivated by looking for the stability controller of saturated time-delay nonlinear systems,one-step anti-windup design based on the indirect linear matrix inequality(LMI)approach is proposed in this paper.First,a class of saturated time-delay nonlinear systems can be reconstructed accurately by using Takagi-Sugeno(T-S)fuzzy model,and then the parallel distributed compensation system with output feedback is used to get the closed-loop control systems.Then,the stability conditions of the closed-loop systems are deduced by using Lyapunov stability theory,and the stability conditions of the closed-loop systems can be converted to two LMIs conditions indirectly by using an equivalent lemma of matrix inequality,then the anti-windup compensation algorithm based on indirect LMI approach is given,meanwhile,the attraction domain estimation and its optimization model are presented.Finally,a simulation example is given to illustrate the proposed method.

关 键 词：一步抗饱和 时滞非线性系统 TAKAGI-SUGENO模糊模型 线性矩阵不等式 并行分布补偿 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]