Adaptive Fuzzy Tracking Control for a Class of Switched Uncertain Nonlinear Systems: An Adaptive State-Dependent Switching Law Method

This paper is concerned with the problem of adaptive fuzzy tracking control for a class of switched uncertain nonlinear systems. The unknown nonlinear functions are approximated by using fuzzy logic systems, and the adaptive backstepping technique is applied to a convex combination of the subsystems. To ensure the continuousness of the Lyapunov function at switching instants, common Lyapunov function (CLF) technique is adopted and the proposed CLF permits switched parameter adaptive laws. Besides, two classes of adaptive laws are proposed, one for designing control laws and one for designing switching law. Then, the common control laws are obtained with the help of the convex combination. Based on the switched adaptive laws, common control laws, a new adaptive state-dependent switching law is proposed. It is shown that the designed state-feedback controllers and switching law can ensure that all the signals remain bounded and the tracking error converges to a small neighborhood of the origin. Moreover, a modified switching law is proposed to avoid Zeno behavior or switching too quickly. Finally, two examples are provided to show the effectiveness of the proposed approaches.