Adaptive critic-based tracking control of non-affine nonlinear discrete-time systems with unknown dynamics

In this paper, the tracking control of a class of general non-affine discrete-time unknown systems represented by the nonlinear autoregressive moving average with eXogenous input (NARMAX) representation is discussed. An equivalent affine-like representation in terms of the tracking error dynamics is first obtained from the original nonaffine nonlinear discrete-time system so that a robust adaptive critic-based neural network controller can be developed. The control scheme consists of an action NN for compensating the unknown system dynamics, and a critic NN to approximate certain strategic utility function and to tune the action NN weights. The NN weights are tuned in an online manner without the need of the knowledge of the system dynamics. By using the standard Lyapunov approach, the uniformly ultimate boundedness (UUB) of the closed-loop tracking error is shown. Simulation results are given to substantiate the theoretical conclusions.