Observer-Based Adaptive Fuzzy Backstepping Control for a Class of Stochastic Nonlinear Strict-Feedback Systems.

In this paper, two adaptive fuzzy output feedback control approaches are proposed for a class of uncertain stochastic nonlinear strict-feedback systems without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the fuzzy state observer, and by combining the adaptive backstepping technique with fuzzy adaptive control design, an adaptive fuzzy output feedback control approach is developed. To overcome the problem of "explosion of complexity" inherent in the proposed control method, the dynamic surface control (DSC) technique is incorporated into the first adaptive fuzzy control scheme, and a simplified adaptive fuzzy output feedback DSC approach is developed. It is proved that these two control approaches can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) in mean square, and the observer errors and the output of the system converge to a small neighborhood of the origin. A simulation example is provided to show the effectiveness of the proposed approaches.