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Neural Networks-Based Adaptive Tracking Control for a Class of High-Order Stochastic Nonlinear Time-Delay Systems

In this paper, neural networks (NNs)-based adaptive backstepping control problem is investigated for uncertain high-order stochastic nonlinear time-delay systems in nonstrict-feedback form. The control design problems appeared in our considered system are 1) high-order nonstrict-feedback structure; 2) completely unknown nonlinear functions; 3) full-state time delays; and 4) stochastic disturbances. The NNs are directly utilized to cope with the completely unknown nonlinear functions and stochastic disturbances existing in systems. The problem raised by full-state time delays is addressed by combining the appropriate Lyapunov-Krasovskii functional with hyperbolic tangent functions. In addition, the variable separation technique is employed to handle the nonstrict-feedback structure of the system. At last, on the basis of stochastic Lyapunov function method, an adaptive neural controller is developed for the considered system. It is shown that the designed adaptive controller can guarantee that all the signals remain semi-globally uniformly ultimately bounded (SGUUB) and the desired signal can be tracked with a small domain of the origin. The simulation results are offered to illustrate the feasibility of the newly designed control scheme.