2-norm optimal design and reduced implementation of Iterative and Repetitive Learning Control

Abstract

This paper studies optimal design of Iterative Learning (ILC) and Repetitive Control (RC) for linear, cycle invariant systems. The optimization is based on minimizing the 2-norm of time signals on a repeating time interval. In contrast to weighting the error and actuating variable, as generally proposed, a different interpretation of the weighting is suggested. This is based on the similarity of 2-norm-optimal designs to Tikhonov regularization, which also makes optimal designs well suited for ill-conditioned systems. The choice of weightings is discussed in comparison to well known ILC designs. Finally, a novel implementation of ILC/RC saving memory and calculation time is presented.