Adaptive dynamic surface control with unmodeled dynamics

Adaptive dynamic surface control is presented for a class of nonlinear system in strict feedback form with unmodeled dynamics. By incorporating the approximation capability of neural networks, the design makes the approach of dynamic surface control be extended to the nonlinear system with unmodeled dynamics, and relaxes the extent of application of the approach of dynamic surface control. By introducing the first order filter, taking advantage of the compact set to overcome the effects of unmodeled dynamics, the explosion of complexity caused by the repeated differentiations of certain nonlinear functions such as virtual controls in traditional backstepping design is avoided. Compared with the existing research, the proposed approach reduces the number of adjustable parameters effectively and does not require the derivative of the virtual control coefficients. By theoretical analysis, the closed-loop control system is shown to be semi-globally uniformly ultimately bounded, with the tracking error converging to a small neighborhood of the origin.