Direct adaptive NN control for a class of discrete-time nonlinear strict-feedback systems

Based on the backstepping technique, a direct adaptive neural network control algorithm is proposed for a class of uncertain nonlinear discrete-time systems in the strict-feedback form. Neural networks are utilized to approximate unknown functions, and a stable adaptive neural backstepping controller is synthesized. It is proven that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of zero by choosing the design parameters appropriately. Compared with the existing results for discrete-time systems, the proposed algorithm needs only less parameters to be adjusted online, therefore, it can reduce online computation burden. A simulation example is employed to illustrate the effectiveness of the proposed algorithm.