Adaptive neural network tracking design for a class of uncertain nonlinear discrete-time systems with unknown time-delay

In this paper, an adaptive neural network tracking control is studied for a class of uncertain nonlinear systems. The studied systems are in discrete-time form and unknown time-delay is considered here. Up to now, the research works on nonlinear discrete-time main focus on systems without time-delay, so the problem of the unknown time-delay will be solved in this paper. Based on the Lipschitz or norm-boundedness assumption of the unknown nonlinearities, the mean-value theorem is utilized to solve the unknown time-delay problem. In order to overcome the noncausal problem, the strict-feedback systems will be transformed into a special form. The radial basis functions neural networks (RBFNN) are utilized to approximate the unknown functions of the systems, the adaptation laws and the controllers are designed based on the transformed systems. By using the Lyapunov analysis, it is proven that the closed-loop system is stable in the sense that semi-globally uniformly ultimately bounded (SGUUB) and the output tracking errors converge to a bounded compact set. A simulation example is used to illustrate the effectiveness of the proposed algorithm.