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 Nussbaum 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 backstepping technique. It is shown that the proposed control scheme guarantees that all the signals of the closed-loop system are semi-globally 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.