Robust adaptive fuzzy output feedback control for stochastic nonlinear systems with unknown control direction

This paper discusses the problem of adaptive fuzzy output feedback control for a class of uncertain stochastic nonlinear strict-feedback systems. The concerned systems have certain characteristics, such as unknown nonlinear functions, dynamical uncertainties, unknown control direction and unmeasured state variables. In this paper, the fuzzy logic systems are used to approximate the unknown nonlinear functions, and a filter state observer is developed for estimating the unmeasured states. To solve the problems of the dynamical uncertainties and the unknown control direction, the changing supply function and Nussbaum function techniques are incorporated into the backstepping recursive design technique, and a new robust adaptive fuzzy output feedback control approach is constructed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded in probability, and also that the observer errors and the output of the system can be regulated to a small neighborhood of the origin by choosing design parameters appropriately. A simulation example is provided to show the effectiveness of the proposed approach.