Adaptive NN control of uncertain nonaffine pure-feedback systems with unknown time-delay

Adaptive dynamic surface control is presented for a class of nonaffine pure-feedback systems with unknown time-delay using neural networks. The problem of "explosion of complexity" in the traditional backstepping algorithm is avoided using dynamic surface control (DSC). The effects of unknown time-delays are eliminated by using appropriate Lyapunov-Krasovskii functionals in the design procedure. The proposed control scheme guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. A simulation example is presented to demonstrate the method.