Adaptive Fuzzy Control for a Class of Stochastic Pure-Feedback Nonlinear Systems With Unknown Hysteresis

This paper addresses the problem of adaptive fuzzy control for a class of stochastic pure-feedback nonlinear systems with unknown direction hysteresis. Compared with the existing researches on hysteresis problem, the stochastic disturbances and the unknown hysteresis are simultaneously considered in the pure-feedback systems. In addition, the hysteresis parameters as well as the direction of hysteresis are unknown. By introducing an auxiliary virtual controller and employing the new properties of Nuss-baum function, the major technique difficulty arising from the unknown direction hysteresis is overcome. Based on the fuzzy logic system's online approximation capability, a novel adaptive fuzzy control scheme is presented via the backstepping technique. It is shown that the proposed control scheme guarantees that all the signals of the closed-loop system are semiglobally uniformly bounded in probability, and the tracking error converges to a neighborhood of the origin in the sense of mean quantic value. Finally, simulation results further demonstrate the effectiveness of the proposed control scheme.