Dynamic Surface Control for Nonlinear Systems with Unknown Control Gains

An adaptive neural network dynamic surface control scheme is proposed to deal with the output tracking control problem of a class of uncertain nonlinear systems with unknown control gain. Based on the backstepping control theory, combined with the idea of reference state, the restrictions on the system nonlinearities which are used to design the virtual controllers are released. The adaptive laws are designed to be smooth to match the prerequisite conditions of applying the Nussbaum gain design techniques in each step. The first order filter is adopted to simplify the procedure of designing the controller, and reduce the complexities and the calculations of the controller. The results of theoretical analysis and simulation show that all the signals in the closed loop systems and the tracking error are semi-globally uniformly ultimately bounded.