Adaptive neural dynamic surface control of nonlinear time-delay systems with model uncertainties

In this paper, the adaptive dynamic surface control (DSC) method is presented for a class of uncertain nonlinear systems with unknown time delays in strict-feedback form. Using the DSC technique, the problem of "explosion of complexity" of the traditional backstepping algorithm can be eliminated and the uncertainties of the unknown time delays are overcome by using appropriate Lyapunov-Krasovskii functionals. Self recurrent wavelet neural networks are employed to observe the arbitrary model uncertainties and the external disturbance online. In addition, it is proved that all the signals in the closed-loop system are semi-globally uniformly bounded. Finally, a simulation result is utilized to illustrate the effectiveness of the proposed control system.