Adaptive Tracking Control for Nonaffine Nonlinear Systems With Zero Dynamics

A direct adaptive neural network tracking control scheme is presented for a class of nonaffine nonlinear systems with zero dynamics. The method does not assume boundedness on the time derivative of a control effectiveness term. Parameters in neural networks are updated using a gradient descent method which designed in order to minimize a quadratic cost function of the error between the unknown ideal implicit controller and the used neural networks controller. The final updated law is a nonlinear function of output error. No robust control term is used in controller. The convergence of parameters and the uniformly ultimately bounded of tracking error and all states of the corresponding closed-loop system are demonstrated by Lyapunov stability theorem.Simulation results illustrate the availability of this method.