Adaptive Neural Networks Control for a Class of Pure-feedback Systems in Discrete-time

In this paper, adaptive neural networks (NNs) control is investigated for a class of nonlinear pure-feedback discrete-time systems by prediction. To overcome the difficulty of nonafflne appearance of control input, the pure-feedback system is transformed into an n-step ahead predictor, and then, implicit function theorem is exploited. NN is employed to approximate the unknown function in the control and the resultant control completely avoids controller singularity problem and achieves semi-global-uniformly-ultimately-boundedness (SGUUB) stability of the closed-loop system. The output tracking error is made within a small neighborhood around zero. The effectiveness of the proposed control approach is demonstrated in the simulation results.