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

Yang Zhu; Emilia Fridman

doi:10.1109/CDC51059.2022.9993185

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

Yang Zhu^*, Emilia Fridman

^*Corresponding author for this work

School of Electrical Engineering

Zhejiang University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-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 language	English
Title of host publication	2022 IEEE 61st Conference on Decision and Control, CDC 2022
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	715-722
Number of pages	8
ISBN (Electronic)	9781665467612
DOIs	https://doi.org/10.1109/CDC51059.2022.9993185
State	Published - 2022
Event	61st IEEE Conference on Decision and Control, CDC 2022 - Cancun, Mexico Duration: 6 Dec 2022 → 9 Dec 2022

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2022-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	61st IEEE Conference on Decision and Control, CDC 2022
Country/Territory	Mexico
City	Cancun
Period	6/12/22 → 9/12/22

Funding

Funders	Funder number
Zhejiang Jianbing Program	2022C01035
Zhejiang Key R&D Program	2021C01198
National Natural Science Foundation of China	61621002
National Natural Science Foundation of China
Israel Science Foundation	673/19
Israel Science Foundation
State Key Laboratory of Industrial Control Technology	ICT2022A08, ICT2022B70
State Key Laboratory of Industrial Control Technology
National Key Research and Development Program of China	2018YFA0703800, 2021YFB1714100
National Key Research and Development Program of China

Access to Document

10.1109/CDC51059.2022.9993185

Cite this

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title = "A Time-delay Approach for Extremum Seeking of Scalar Dynamical Systems",

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.",

author = "Yang Zhu and Emilia Fridman",

note = "Publisher Copyright: {\textcopyright} 2022 IEEE.; 61st IEEE Conference on Decision and Control, CDC 2022 ; Conference date: 06-12-2022 Through 09-12-2022",

year = "2022",

doi = "10.1109/CDC51059.2022.9993185",

language = "אנגלית",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "715--722",

booktitle = "2022 IEEE 61st Conference on Decision and Control, CDC 2022",

address = "ארצות הברית",

}

Zhu, Y & Fridman, E 2022, A Time-delay Approach for Extremum Seeking of Scalar Dynamical Systems. in 2022 IEEE 61st Conference on Decision and Control, CDC 2022. Proceedings of the IEEE Conference on Decision and Control, vol. 2022-December, Institute of Electrical and Electronics Engineers Inc., pp. 715-722, 61st IEEE Conference on Decision and Control, CDC 2022, Cancun, Mexico, 6/12/22. https://doi.org/10.1109/CDC51059.2022.9993185

A Time-delay Approach for Extremum Seeking of Scalar Dynamical Systems. / Zhu, Yang; Fridman, Emilia.
2022 IEEE 61st Conference on Decision and Control, CDC 2022. Institute of Electrical and Electronics Engineers Inc., 2022. p. 715-722 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2022-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - 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.

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

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