On periodic solutions of adaptive systems in the presence of periodic forcing terms
type: Item
instance of: scholarly article
title: On periodic solutions of adaptive systems in the presence of periodic forcing terms
zbMATH Open document ID: 0712.93031
DOI: 10.1007/BF02551376
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 1990-01-01T00:00:00Z
review text: This paper studies solutions of adaptive feedback loops in the presence of unmodeled dynamics if the discrete-time linear plant. It assumes that the reference output is periodic with period K. The aim is to find K- periodic solutions of the adaptive system and study their stability. Sufficient conditions to have K-periodic solutions are derived. Also, the stability of these solutions is studied assuming that adaptation is slow. A wide class of direct adaptive controllers is used for checking the sufficient conditions for the existence of a periodic solution. It is proved that ``almost always'' the periodic solution exists, but no tools to study its stability, except in the exact modeling case, are available. The present study would be a first step toward a complete description of the behavior of an adaptive controller in feedback with a high-order linear plant.
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C55
zbMATH DE Number: 4172853
zbMATH Keywords: adaptive feedback loops
zbMATH Keywords: unmodeled dynamics
zbMATH Keywords: periodic solution
author: Jean-Baptiste Pomet
author: Jean-Michel Coron
author: Laurent Praly
reviewed by: Petre Stoica
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02551376
OpenAlex ID: W2129575062
description: scientific article; zbMATH DE number 4172853