A Robust Time-Delay Approach to Continuous-Time Extremum Seeking for Multi-Variable Static Map

Xuefei Yang, Emilia Fridman

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

Abstract

In this article, we introduce a time-delay approach to gradient-based extremum seeking (ES) in the continuous domain for n-dimensional (nD) static quadratic maps. As in the recently introduced (for 2D maps in the continuous domain), we transform the system to the time-delay one (neutral type system). This system is Oϵ. 'perturbation of the averaged linear ODE system. We further explicitly present the neutral system as the linear ODE, where O(ϵ)-terms are considered as disturbances with distributed delays of the length of the small parameter ϵ. Quantitative (for uncertain map) and qualitative (for unknown map) practical stability analyses are provided by employing a variation of constants formula that greatly simplifies the results compared to the previously used Lyapunov-Krasovskii (L-K) method. The new approach also simplifies the conditions and improves the results. Examples from the literature illustrate the efficiency of the new approach, allowing essentially large uncertainty of the Hessian matrix with bounds on ϵ that are not too small.

Original languageEnglish
Title of host publication2023 62nd IEEE Conference on Decision and Control, CDC 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6768-6773
Number of pages6
ISBN (Electronic)9798350301243
DOIs
StatePublished - 2023
Event62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore
Duration: 13 Dec 202315 Dec 2023

Publication series

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

Conference

Conference62nd IEEE Conference on Decision and Control, CDC 2023
Country/TerritorySingapore
CitySingapore
Period13/12/2315/12/23

Keywords

  • averaging
  • Extremum seeking
  • practical stability
  • time-delay

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