Adaptive neural output-feedback control for nonstrict-feedback stochastic nonlinear time-delay systems with hysteresis

This paper proposes an adaptive neural outputfeedback controller for a class of nonstrict-feedback stochastic nonlinear time-delay systems with unknown backlash-like hysteresis. First, a state observer is established for estimating the unmeasured states. Second, an appropriate Lyapunov-Krasovskii functional is used to compensate the unknown time-delay terms, and the neural network is employed to approximate the unknown nonlinear functions. At last, an output-feedback adaptive neural control scheme is constructed by using Lyapunov stability theory and backstepping technique. It is shown that the designed neural controller can ensure that all the signals in the closed-loop system are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. Two examples are presented to further show the effectiveness of the proposed approach.