Fuzzy-Approximation-Based Adaptive Output-Feedback Control for Uncertain Nonsmooth Nonlinear Systems

This paper proposes a solution to adaptive output-feedback control for a class of nonsmooth nonlinear systems. First, the concept of semiglobally uniformly ultimately bounded (SGUUB) stability that has been widely used for smooth nonlinear systems with lower triangular systems is extended to the nonsmooth systems. Then by resorting to set-valued maps and set-valued derivatives, a new Lyapunov criterion ensuring the SGUUB stability is developed for nonsmooth nonlinear systems, which establishes the theory foundation for the subsequent backstepping control design. With the help of Cellina approximate selection theorem and smooth approximation theorem for Lipschitz functions, the system under investigation is first transformed into an equivalent model. In the sequel, exploring some efficient techniques, an adaptive fuzzy output-feedback controller is constructed for the systems under consideration by utilizing an appropriate observer and the approximation ability of fuzzy systems. Finally, a numerical example is given to show the effectiveness of the proposed control method.