A Time-delay Approach for Extremum Seeking of Scalar Dynamical Systems

Yang Zhu*, Emilia Fridman

*Corresponding author for this work

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

Abstract

Recently a new time-delay approach was introduced for extremum seeking (ES), but the results were confined to static maps. In the present paper, the time-delay approach is extended for the 1st time to ES of dynamic maps in the case of scalar plants. We not only provide a precise perturbed system of ES without any approximation, but also suggest a direct Lyapunov-Krasovskii method for the transformed time-delay plant to find efficient stability conditions for the closed-loop ES system in the form of linear matrix inequalities (LMIs). Differently from the approaches based on classical averaging and Lie brackets, we provide the quantitative bounds on the frequency and the resulting extremum seeking error, under assumption that the extremum point, the extremum value and the Hessian are uncertain from some known intervals.

Original languageEnglish
Title of host publication2022 IEEE 61st Conference on Decision and Control, CDC 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages715-722
Number of pages8
ISBN (Electronic)9781665467612
DOIs
StatePublished - 2022
Event61st IEEE Conference on Decision and Control, CDC 2022 - Cancun, Mexico
Duration: 6 Dec 20229 Dec 2022

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2022-December
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference61st IEEE Conference on Decision and Control, CDC 2022
Country/TerritoryMexico
CityCancun
Period6/12/229/12/22

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