Continuous-time Extremum Seeking for Scalar Systems via a Time-Delay Approach to Averaging

Yang Zhu, Emilia Fridman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In this paper, we present a constructive approach to continuous-time extremum seeking (ES) by using a time-delay approach to averaging. We consider gradient-based ES of static maps in the case of single-input, and we study two ES methods: the classical one and a more recent bounded ES method. By transforming the ES dynamics into a time-delay system where the delay is the period of dither, we derive the practical stability conditions for the resulting time-delay system. The time-delay system stability guarantees the stability of the original ES plant. Under the assumption of some known bounds on the extremum value and the Hessian, the time-delay approach provides a quantitative calculation on the lower bound of the frequency and on the resulting ultimate bound. We also give a bound on the neighbourhood of the extremum point starting from which the solution is ultimately bounded. When the Hessian and the extremum value bounds are unknown, we provide, for the first time, the asymptotic ultimate bound in terms of the frequency in the case of bounded ES. Moreover, our explicit bound on the seeking error of ES control systems allows to select appropriate tuning parameters (such as dither frequency, magnitude, and control gain).

Original languageEnglish
Title of host publication60th IEEE Conference on Decision and Control, CDC 2021
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages352-359
Number of pages8
ISBN (Electronic)9781665436595
DOIs
StatePublished - 2021
Event60th IEEE Conference on Decision and Control, CDC 2021 - Austin, United States
Duration: 13 Dec 202117 Dec 2021

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2021-December
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference60th IEEE Conference on Decision and Control, CDC 2021
Country/TerritoryUnited States
CityAustin
Period13/12/2117/12/21

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