Adaptive fuzzy backstepping output feedback control for a class of uncertain stochastic nonlinear system in pure-feedback form

This paper is concerned with the problem of adaptive fuzzy output feedback for a class of uncertain stochastic pure-feedback nonlinear systems with immeasurable states. With the help of fuzzy logic systems to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. By incorporating the filtered signals into the backstepping recursive design, a fuzzy adaptive output feedback control scheme is developed. It is proven that all the signals of the closed-loop system are bounded in probability, and also that the observer errors and the output of the system 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.