Fuzzy-neural adaptive iterative learning control for a class of nonlinear discrete-time systems

In this paper, a fuzzy neural network based adaptive iterative learning controller (AILC) for a class of nonlinear discrete-time plants which can repeat a given task over a finite time interval is proposed. To overcome the function approximation errors, initial resetting errors and undesired chattering behavior, a time-varying boundary layer is introduced to design an auxiliary error function. Based on the auxiliary error function, the fuzzy neural networks in this AILC are used as an approximators to compensate for the plant unknown nonlinearities. Since the optimal parameters for a good function approximation are unavailable, the adaptive algorithms are derived to guarantee the closed-loop stability and learning convergence. Based on a Lyapunov like analysis, we show that all the adjustable parameters as well as internal signals are bounded for all iterations. The norm of output tracking error vector will asymptotically converge to a residual set bounded by the width of boundary layer as iteration goes to infinity.