Observer-based adaptive fuzzy backstepping control of uncertain nonlinear pure-feedback systems

In this paper, a new fuzzy adaptive control approach is developed for a class of SISO uncertain pure-feedback nonlinear systems with immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions; and the filtered signals are introduced to circumvent algebraic loop systems encountered in the implementation of the controller, and a fuzzy state adaptive observer is designed to estimate the immeasurable states. By combining the adaptive backstepping technique, an adaptive fuzzy output feedback control scheme is developed. It is proven that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the observer and tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters. Simulation studies are included to illustrate the effectiveness of the proposed approach.