This paper aims to analyze the problem of adaptive neural network (NN) tracking control for a class of switched stochastic nonlinear pure-feedback systems with unknown direction hysteresis. In the light of recent studies on the hysteresis phenomenon in the field of nonlinear switched systems, this work focuses on Bouc-Wen hysteresis model with unknown parameters and direction conditions. To simplify the control design, the following procedure is applied. Prior to tackling the unknown direction hysteresis problem based on the Nussbaum function and the backstepping techniques, the pure-feedback structure difficulty is governed by the mean value theorem. Furthermore, an optimized adaptation method is utilized to cope with computational burden. Universal approximation capability of radial basis function NNs and Lyapunov function method are synthesized to develop an adaptive NN tracking control scheme. It is demonstrated that under arbitrary deterministic switching, the presented controller can guarantee that all signals in the closed-loop system are semi-globally uniformly ultimately bounded in probability and the tracking error converges to a neighborhood of the origin. Finally, two simulation examples are given to illustrate the advantages of the proposed control design approach.

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