Neural adaptive dynamic surface control for mismatched uncertain nonlinear systems with nonlinear feedback errors

This paper addresses a new nonlinear gain feedback based neural adaptive dynamic surface control (DSC) method for a class of strict feedback nonlinear systems in the presence of uncertainties and external disturbances. Besides circumventing the problem of complexity explosion, the nonlinear gain feedback technique brings a self-regulation ability into the pioneering DSC method to improve the dynamic performance of the resulted closed-loop system. Neural networks are used to online approximating the uncertainties, the over-fitting problem occurs with small probability since the signals obtained by NNs are also handled using nonlinear gain function. It is proved rigorously by Lyapunov stability theorem that all the closed-loop signals are kept semi-globally uniformly ultimately bounded, the output tracking error and the optimal neural weight vector estimation error can all be adjusted to arbitrarily small around zero characterized by design parameters in an explicit way. Furthermore, the method proposed can be extended to the control of multiple-input-multiple-output system trivially. Comparative simulation results are presented to demonstrate the effectiveness of the proposed method.