Adaptive fuzzy control design and applications of uncertain stochastic nonlinear systems with input saturation

In this paper, the problem of adaptive fuzzy output feedback control is investigated for a class of uncertain stochastic nonlinear systems. The stochastic nonlinear systems under study have unknown nonlinear uncertainties, unmodeled dynamics, input saturation and without the direct measurement of state variables. Fuzzy logic systems and a smooth function are first utilized to approximate the unknown nonlinear functions and the input saturation, respectively, and then a fuzzy state observer is designed to estimate the unmeasured states. By combining the adaptive backstepping design technique with the dynamic surface control (DSC) design technique and using the concept of the dynamical signal, a new adaptive fuzzy output feedback tracking control approach is developed. It is proved that all the variables involved in the closed-loop system are semi-globally uniformly ultimately bounded (SUUB) in probability, and also that both observer errors and tracking errors converge to a small neighborhood of the origin by appropriate selecting the design parameters. The proposed adaptive fuzzy control approach is finally applied to the two-stage chemical reactor with recycle streams, and achieves the satisfactory control performance.