Adaptive fuzzy tracking control of switched uncertain nonlinear systems with unstable subsystems

Abstract

This paper is concerned with the problem of adaptive fuzzy tracking control for a class of switched uncertain nonlinear systems where the solvability of the fuzzy tracking control problem for subsystems is unnecessary. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a new adaptive fuzzy tracking control technique for the problem under study is set up. Based on the technique above, we design a switching law and construct adaptive fuzzy controllers of subsystems explicitly by a recursive design algorithm to guarantee that all the signals in the resulting closed-loop system remain bounded and the system output of the closed-loop system converges to a small neighborhood of the reference signal. Multiple Lyapunov functions are exploited to get out of the conservativeness caused by adoption of a common Lyapunov function for all subsystems, which is commonly required when applying the backstepping-like recursive design scheme. A mass–spring–damper system is provided to demonstrate the effectiveness of the proposed design method.