A Time-delay Approach for Sampled-data and Delayed Scalar Extremum Seeking

Yang Zhu, Emilia Fridman, Tiago Roux Oliveira

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

Abstract

This paper proposes a constructive approach for sampled-data delayed extremum seeking (ES) by using two time-delay approaches: one to averaging and another one to sampled-data control. We first investigate the continuous-time ES with square wave dithers and then expand the proposed time-delay method to its sampled-data implementation with constant delay. By transforming the ES system to a time-delay system, we have developed an improved stability analysis via a novel Lyapunov-Krasovskii functional (LKF). We derive the practical stability conditions in terms of linear matrix inequalities (LMIs) for the resulting time-delay system. Under the assumption of some known bounds on the extremum value of the map and its Hessian, the time-delay approach offers a quantitative calculation on the upper bounds of the dither-sampling period and the constant delays that the ES system is able to tolerate, as well as the ultimate bound of the extremum seeking error. The proposed method also provides a bound on the initial deviation starting from which the solution is ultimately bounded.

Original languageEnglish
Title of host publication60th IEEE Conference on Decision and Control, CDC 2021
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6073-6080
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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