Adaptive Fuzzy Prescribed Performance Control for MIMO Stochastic Nonlinear Systems

This paper investigates the adaptive fuzzy output feedback prescribed performance control (PPC) problem for multiple-input and multiple-output (MIMO) stochastic nonlinear systems in the nonstrict-feedback form. The study of MIMO nonlinear stochastic systems is assumed to have non-structural uncertainty, unknown control directions, and unknown dead zones. The fuzzy logic systems are adopted to approximate the unknown nonlinear functions, and a state observer is designed to estimate the unmeasured states. By combining backstepping recursive design principle with PPC theory, an observer-based adaptive fuzzy prescribed performance tracking control method is presented. In order to overcome the problem of unknown control directions in nonlinear stochastic systems, the Nussbaum gain function is introduced into adaptive fuzzy control design algorithm. The stability is proven based on the Lyapunov stability theory, which demonstrated that all the signals of the closed-loop systems are semi-globally uniformly ultimately bounded (SGUUB) in probability and the tracking errors remain a small neighborhood of the origin within the prescribed performance boundeds. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed approach.