Stability of extremum seeking feedback for general nonlinear dynamic systems
type: Item
instance of: scholarly article
title: Stability of extremum seeking feedback for general nonlinear dynamic systems
zbMATH Open document ID: 0986.93039
DOI: 10.1016/S0005-1098(99)00183-1
author: Hsin-Hsiung Wang
author: Miroslav Krstic
published in: Automatica
publication date: 2002-06-13T00:00:00Z
review text: While the mainstream methods of adaptive control (both linear and nonlinear) deal only with regulation to known set points or reference trajectories, in many applications the set point should be selected to achieve a maximum of an uncertain reference-to-output equilibrium map. The techniques of the so-called ``extremum control'' or ``self-optimizing control'' developed for this problem in the 1950s--1960s have long gone out of fashion in the theoretical control literature because of the difficulties that arise in a rigorous analytical treatment. The main contribution of this paper is that it provides a rigorous proof of stability for an extremum seeking feedback scheme. The tools of averaging and singular perturbations are employed to show that solutions to the closed-loop system converge to a small neighborhood of the extremum of the equilibrium map. The size of the neighborhood is inversely proportional to the adaptation gain and the amplitude and the frequency of a periodic signal used to achieve extremum seeking. This analysis highlights a fundamentally nonlinear mechanism of stabilization in an extremum seeking loop.
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93C70
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 1437554
zbMATH Keywords: adaptive control
zbMATH Keywords: extremum seeking feedback
zbMATH Keywords: averaging
zbMATH Keywords: singular perturbations
zbMATH Keywords: periodic signal
zbMATH Keywords: stabilization
Wikidata QID: Q59622079
reviewed by: Vasile Dragan
MaRDI profile type: Publication
cites work: Q3631315
cites work: Q3799870
cites work: Q3272026
cites work: Asymptotic methods for investigating a class of forced states in extremal systems
cites work: Asymptotic methods for investigating quasistationary states in continuous systems of automatic optimization
cites work: Continuous extremum control systems in the presence of random noise
cites work: Q3910397
cites work: Optimizing bioreactors by extremum seeking
full work available at URL: s0005-1098(99)00183-1
OpenAlex ID: W2095062552
DBLP publication ID: journals/automatica/KrsticW00
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description: scientific article; zbMATH DE number 1437554