Nonlinear gain feedback adaptive DSC for a class of uncertain nonlinear systems with asymptotic output tracking

Abstract

This paper proposes an adaptive dynamic surface controller with nonlinear gain feedback for a class of uncertain nonlinear systems to achieve the asymptotic output tracking. A nonlinear filter is designed to eliminate the effects raised by the boundary layer error at each step in the dynamic surface control (DSC) procedure. Meanwhile, a new nonlinear gain function, which can regulate the control ability automatically, is designed to improve the dynamic performance of system. Then, an adaptive controller is explicitly designed to achieve the asymptotic output tracking. Moreover, a novel Lyapunov function is designed to analyze the stability of the proposed algorithm. The proposed DSC algorithm not only can avoid the inherent problem of “explosion of complexity” in the back-stepping procedure, but also can achieve the asymptotic output tracking and improve the dynamic performance. Some simulations are shown to demonstrate the effectiveness and advantages of the proposed controller.