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Summary: Iterative learning control for singularly perturbed systems
Konstantin E. Avrachenkov \Lambda Anatoly A. Pervozvanski y
March 14, 1999
Abstract
The singularly perturbed systems are described by differential equations with a small
parameter near higher derivatives. It turns out that most of known iterative learning con
trol algorithms diverge in the presence of singular perturbations. The aim of the present
paper is to construct learning control algorithms that are able to overcome this problem.
Our approach is based on weak convergence conditions that take into account the whole
range of frequency response characteristic in contrast to traditional convergence condi
tions based on the rough H1 norm. The first two proposed methods employ the analog
and digital filtering. Whereas the learning operator of the third method approximates the
inverse of the regular part of the system and at the same time appears to be a lowpass
filter. The simulation of the algorithms for a benchmark model confirms all theoretical
considerations.
Key words: iterative learning control, singular perturbations, filtering.
1 Introduction
In this paper we investigate the convergence of learning control algorithms in the presence of
singular perturbations. By singular perturbations we mean the perturbations that cause the
increase of system dimension. In particular, if a system is described by differential equations,
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