An Iterative Learning Control for Noisy Systems by Using Linear Neural Networks

Abstract

By applying a linear neural network, an iterative learning control is described for noisy CARMA (Controlled Autoregressive Moving Average) systems. The developed controller has a form of direct controller in a stochastic environment, while the usual iterative controller has a form of discrete observer in a determine-istic environment. Thus, the present iterative controller can treat with the case of noisy measurements. First, we describe the system considered here and state some assumptions to solve the problem. Next, the model of inverse dynamics is derived and the off-line iterative learning rule is explained by using the delta rule. Then, we show a neural controller, under the situation where the measurement noise is assumed to be known. Furthermore, we describe the method to estimate the noise process on-line by using the associated regular dynamics. Finally, we show some simulation examples to illustrate the features of the present controller. In particular, we shall discuss the results from the view points of the initial connec-tions weights and the generalizability of linear neural networks to some different or untrained reference signals.