Stable adaptive fuzzy control of nonlinear systems using small-gain theorem and LMI approach  

作　　者：Haibo JIANG Jianjiang YU Caigen ZHOU 

机构地区：[1]School of Mathematics, Yancheng Teachers University, Yancheng Jiangsu 224051, China [2]School of Information Science and Technology, Yancheng Teachers University, Yancheng Jiangsu 224002, China

出　　处：《控制理论与应用（英文版）》2010年第4期527-532,共6页

基　　金：supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No.07KJB510125,08KJD510008);the Natural Science Foundation of Yancheng Teachers University(No.07YCKL062,08YCKL053)

摘　　要：A new design scheme of stable adaptive fuzzy control for a class of nonlinear systems is proposed in this paper.The T-S fuzzy model is employed to represent the systems.First,the concept of the so-called parallel distributed compensation （PDC） and linear matrix inequality （LMI） approach are employed to design the state feedback controller without considering the error caused by fuzzy modeling.Sufficient conditions with respect to decay rate α are derived in the sense of Lyapunov asymptotic stability.Finally,the error caused by fuzzy modeling is considered and the input-to-state stable （ISS） method is used to design the adaptive compensation term to reduce the effect of the modeling error.By the small-gain theorem,the resulting closed-loop system is proved to be input-to-state stable.Theoretical analysis verifies that the state converges to zero and all signals of the closed-loop systems are bounded.The effectiveness of the proposed controller design methodology is demonstrated through numerical simulation on the chaotic Henon system.A new design scheme of stable adaptive fuzzy control for a class of nonlinear systems is proposed in this paper.The T-S fuzzy model is employed to represent the systems.First,the concept of the so-called parallel distributed compensation （PDC） and linear matrix inequality （LMI） approach are employed to design the state feedback controller without considering the error caused by fuzzy modeling.Sufficient conditions with respect to decay rate α are derived in the sense of Lyapunov asymptotic stability.Finally,the error caused by fuzzy modeling is considered and the input-to-state stable （ISS） method is used to design the adaptive compensation term to reduce the effect of the modeling error.By the small-gain theorem,the resulting closed-loop system is proved to be input-to-state stable.Theoretical analysis verifies that the state converges to zero and all signals of the closed-loop systems are bounded.The effectiveness of the proposed controller design methodology is demonstrated through numerical simulation on the chaotic Henon system.

关 键 词：Nonlinear control Fuzzy control Adaptive control Small-gain theorem Input-to-state stability 

分 类 号：TP273.2[自动化与计算机技术—检测技术与自动化装置] TP13[自动化与计算机技术—控制科学与工程]