Adaptive Tracking Control for a Class of Switched Nonlinear Systems Under Asynchronous Switching

This paper investigates the problem of adaptive fuzzy tracking control for a class of switched uncertain nonlinear systems under asynchronous switching. Inspired by the discretized Lyapunov function technique, a class of time-schedule Lyapunov functions (TSLFs) is first proposed to analyze the stability under asynchronous switching. Then, based on the proposed TSLF, novel observer and adaptive laws with time-schedule observer gain and design parameters are proposed to deal with asynchronous switching. Moreover, a switched command filter with the virtual control functions as input is proposed to avoid “the explosion of complexity” and tracking error jumps, which make the stability analysis difficult. It is shown that under the proposed controller, all the signals of the closed-loop system are bounded, and the tracking errors converge to a small neighborhood of zero in spite of asynchronous switching. Finally, the effectiveness of the proposed method is illustrated through two illustrative examples.