Fuzzy Approximation Based Asymptotic Tracking Control for a Class of Uncertain Switched Nonlinear Systems

The problem of asymptotic tracking control for a class of uncertain switched nonlinear systems under fuzzy approximation framework is solved in this paper. Superior to most existing results based on fuzzy adaptive control strategy that can only achieve bounded error tracking performance, our proposed control scheme can guarantee the local asymptotic tracking performance for the uncertain switched nonlinear systems under consideration. This is accomplished by constructing a nonsmooth Lyapunov function and introducing a novel discontinuous controller with dynamic feedback compensator in the design procedure. Meanwhile, some concepts, such as differential inclusion and set-valued map, are introduced to theoretically verify the local asymptotic tracking performance of the systems with our proposed controller. With the help of set-valued Lie derivative, the common virtual control functions, the desired controller, and the adaptive laws can be precisely constructed. Finally, simulation results are given to show the effectiveness of the proposed method.