Adaptive NN control for a class of stochastic nonlinear systems with unmodeled dynamics using DSC technique

This paper investigates the problem of adaptive neural networks output feedback control for a class of stochastic nonlinear system with unmodeled dynamics and unmeasured states. To avoid the problem of ‘explosion of complexity’ inherent in the conventional backstepping design procedure, the dynamic surface control (DSC) technique is applied to the control design of the investigated systems with unmodeled dynamics. Also, the reduced-order observer is designed to estimate those unmeasured states. Then, with the concept of input-to-state practical stability (ISpS) and nonlinear small-gain theorem extending to the stochastic case, together with DSC design technique, an adaptive neural network (NN) output feedback controller is proposed. The outstanding feature of the proposed scheme is that, only one neural network is employed to compensate for all unknown nonlinear functions, so that the designed controller is much simpler than the existing results. It is shown that the solutions of the closed-loop system are bounded in probability, and the output of the system converges to a small neighborhood of the origin by choosing suitable design parameters. The simulation results demonstrate the performance of the proposed scheme.