A time-delay approach to stabilization by extremum seeking controller via simplified ISS analysis

Jin Zhang, Emilia Fridman, Xuefei Yang

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

Abstract

We study stabilization of linear uncertain systems under unknown control directions using a bounded extremum seeking controller with a small parameter. We consider a small time-varying measurement delay. By using the recently proposed time-delay approach to Lie-Brackets-based averaging, we transform the closed-loop system to a time-delay (neutral type) one, which has a form of perturbed Lie brackets system. The input-to-state stability (ISS) of the time-delay system guarantees the same for the original one. Differently from the existing analysis via Lyapunov-Krasovskii (L-K) method, we transform the neutral system to an ordinary differential equation (ODE) with delayed perturbations and employ variation of constants formula that greatly simplifies the analysis and leads to simpler stability conditions. Two numerical examples illustrate that the proposed method allows essentially larger parameter uncertainties with bounds on the small parameter and time-delay that are not too small.

Original languageEnglish
Title of host publicationIFAC-PapersOnLine
EditorsHideaki Ishii, Yoshio Ebihara, Jun-ichi Imura, Masaki Yamakita
PublisherElsevier B.V.
Pages4289-4294
Number of pages6
Edition2
ISBN (Electronic)9781713872344
DOIs
StatePublished - 1 Jul 2023
Event22nd IFAC World Congress - Yokohama, Japan
Duration: 9 Jul 202314 Jul 2023

Publication series

NameIFAC-PapersOnLine
Number2
Volume56
ISSN (Electronic)2405-8963

Conference

Conference22nd IFAC World Congress
Country/TerritoryJapan
CityYokohama
Period9/07/2314/07/23

Keywords

  • extremum seeking
  • Lie-brackets-based averaging
  • Time-delay

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