A Time-delay Approach for Extremum Seeking of Nonlinear Static Maps

Yang Zhu*, Emilia Fridman

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

Abstract

This paper develops a constructive time-delay approach to averaging for gradient-based extremum seeking (ES) control of nonlinear static maps of non-quadratic form. Under the assumption that some prior knowledge of the nonlinear map with its derivatives is available, for the first time, we derive a quantitative analysis for ES close-loop systems with upper bounds on the tuning parameter that preserves the exponential stability and on the convergence error of extremum seeking. By transforming the ES system into a time-delay neutral type system with distributed delays, the developed method gives an accurate perturbed system of ES without employing any approximate calculation, and suggests a direct Lyapunov-Krasovskii approach in the form of linear matrix inequalities (LMIs), for the transformed time-delay plant to derive efficient stability conditions .

Original languageEnglish
Pages (from-to)258-263
Number of pages6
JournalIFAC-PapersOnLine
Volume56
Issue number1
DOIs
StatePublished - 1 Jan 2023
Event12th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2022 - Canberra, Australia
Duration: 4 Jan 20236 Jan 2023

Funding

FundersFunder number
Zhejiang Jianbing Program2022C01035
Zhejiang Key R&D Program2021C01198
National Natural Science Foundation of China61621002
Israel Science Foundation673/19
State Key Laboratory of Industrial Control TechnologyICT2022A08, ICT2022B70
National Key Research and Development Program of China2018YFA0703800, 2021YFB1714100

    Keywords

    • Extremum Seeking
    • Non-quadratic
    • Nonlinear
    • Static
    • Time-delay

    Fingerprint

    Dive into the research topics of 'A Time-delay Approach for Extremum Seeking of Nonlinear Static Maps'. Together they form a unique fingerprint.

    Cite this