Iterative learning identification and control for dynamic systems described by NARMAX model

A new iterative learning controller is proposed for a general unknown discrete time-varying nonlinear non-affine system represented by NARMAX (Nonlinear Autoregressive Moving Average with eXogenous inputs) model. The proposed controller is composed of an iterative learning neural identifier and an iterative learning controller. Iterative learning control and iterative learning identification are integrated in each iteration. A multi-layer neural network is used for identification. Since the system considered in this paper is time-varying, the proposed neural identifier also is time-varying. The weights of the neural identifier are updated at each iteration, so both tracking performance and identification are improved at each iteration simultaneously. The structure of the proposed neural network used for identification system is affine in control input. Then new iterative learning control law based on the neural identifier is proposed and applied to the system. It should be mentioned that the proposed integrated algorithm has a faster, better and more accurate performance when compared with other iterative learning control algorithms proposed for similar systems. Convergence of both the trajectory tracking error and identification error is guaranteed along the iteration domain with repeating the process within a time-limited range. Simulation and comparison results easily approve the effectiveness of the proposed method.