Bounded Extremum Seeking for Single-Variable Static Map with Large Measurement Delay via Time-Delay Approach to Averaging

Xuefei Yang, Emilia Fridman, Bowen Zhao

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

Abstract

In this paper, we present a time-delay approach to gradient-based bounded extremum seeking (ES) with large measurement constant delay, for an unknown single-input static quadratic map. We assume that the extremum point and the Hessian H belong to known intervals, whereas the sign of H is known. We apply a time-delay approach to the bounded ES system and arrive at the neutral type system with a nominal linear delayed system. We present the latter system as a retarded one and employ variation of constants formula for practical stability analysis. Explicit conditions in terms of simple scalar inequalities depending on tuning parameters and delay are established to guarantee the practical stability of the bounded ES control systems. Given any delay and neighborhood of the extremum point and through the solution of the constructed inequalities, we find lower bounds on the dither period that ensures the practical stability.

Original languageEnglish
Title of host publication2023 62nd IEEE Conference on Decision and Control, CDC 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3664-3669
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
  • Bounded extremum seeking
  • practical stability
  • time- delay

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