Adaptive control for a class of nonlinear discrete-time systems using neural networks

In this paper, the adaptive control problem is studied for a class of discrete-time unknown nonlinear systems with general relative degree in the presence of bounded disturbances. To derive the feedback control, a causal state-space model of the plant is obtained. By using an NN observer to estimate the unavailable but predictable states of the system, a Lyapunov-based adaptive state feedback NN controller is proposed. The state feedback control avoids the possible singularity problem in adaptive nonlinear control. The closed-loop system is proven to be semi-globally uniformly ultimately bounded (SGUUB). An arbitrarily small tracking error can be achieved if the size of neural networks is chosen large enough, and the control performance of the closed-loop system is guaranteed by suitably choosing the design parameters.