Fuzzy output-feedback control for nonlinear stochastic systems with unknown-time-delays

In this paper, an observer-based adaptive fuzzy backstepping control approach is proposed for a class of uncertain nonlinear stochastic systems with the immeasurable states and unknown-time-delays. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. By combining the backstepping design technique, an observer-based adaptive fuzzy control method is developed. It is proved that the proposed adaptive fuzzy control approach can not only guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) in mean square, but also the output of the system converge to a small neighborhood of the origin.