Summary: Iterative learning control for singularly perturbed systems
Konstantin E. Avrachenkov 1 Anatoly A. Pervozvanski 2
Abstract
The singularly perturbed systems are described by dif­
ferential equations with a small parameter near higher
derivatives. It turns out that most of known itera­
tive learning control algorithms diverge in the presence
of singular perturbations. The aim of the present pa­
per 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 conditions based
on the rough H1 norm. The first two proposed meth­
ods 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 simula­
tion of the algorithms for a benchmark model confirms
all theoretical considerations.

Source: Avrachenkov, Konstantin - INRIA Sophia Antipolis

Collections: Computer Technologies and Information Sciences