Design and Analysis of Fuzzy-Neural Discrete Adaptive Iterative Learning Control for Nonlinear Plants

In this paper, a fuzzy neural network (FNN) based discrete adaptive iterative learning controller (AILC) is proposed for a class of discrete-time uncertain nonlinear plants which can repeat a given task over a finite time sequence. Compared with the existing discrete AILC schemes, the proposed strategy can be applied to the discrete-time uncertain nonlinear plants with not only initial resetting errors and iteration- varying desired trajectory, but also random bounded disturbances and unknown non-Lipschitz plant nonlinearities. Two FNNs are used as approximators to compensate for the unknown plant nonlinearities. To overcome the function approximation error and possibly large random bounded disturbance, a time-varying boundary layer is introduced to design an auxiliary error function. The auxiliary error function is then utilized to derive the adaptive laws since the optimal FNN parameters for a good function approximation and the optimal width of time-varying boundary layer are unavailable. By using a Lyapunov like analysis, we show that the closed-loop is stable in the sense that the adjustable parameters and internal signals are bounded for all the iterations. Furthermore, learning performance is guaranteed in the sense that the norm of output tracking error vector will asymptotically converge to a residual set which is bounded by the width of boundary layer.