A Relationship between Iterative Learning Control Using the Gradient Method and Stable Inversion

Abstract

Iterative learning control (ILC) obtains a desired input trajectory by repeating trials. Stable Inversion constructs a bounded input for desired output trajectory by using the non-causal inverses for non-minimum phase systems. In this paper, we investigate a relationship between the ILC using adjoint systems and the stable inversion. In order to clarify this relationship, we must extend the trial interval from the finite time interval [T₀, T_f] to the infinite time interval (-∞, ∞). However, when ILC is applied to actual systems, it is impossible to carry out the trial on an infinite time interval. So, the trial interval is necessarily truncated to the finite interval. Hence, we investigate the effect of the truncation on tracking performance.