Adaptive tracking control for uncertain switched stochastic nonlinear pure-feedback systems with unknown backlash-like hysteresis

In this paper, an adaptive tracking control problem is studied for a class of switched stochastic nonlinear pure-feedback systems with unknown backlash-like hysteresis under arbitrary switching. The mean-value theorem is used to overcome the difficulty arising from the pure-feedback structure. Based on neural networks' approximation capability, an adaptive tracking control approach is developed via the adaptive backstepping technique and common Lyapunov function method. It is proved that the proposed control scheme can guarantee that all signals in the closed-loop system are semi-globally uniformly ultimately bounded in probability and the tracking error converges to an adjustable neighborhood of the origin. Finally, a simulation example further shows the effectiveness of the presented control scheme.