A Time-Delay Approach to Extremum Seeking with Measurement Noise

Bowen Zhao*, Xuefei Yang*, Emilia Fridman

*Corresponding author for this work

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


In this paper, we present a time-delay approach to extremum seeking (ES) corrupted by white noise for uncertain static quadratic maps. We first apply a time-delay approach to the ES system and arrive at a neutral type time-delay system with stochastic perturbations. Then we further present the latter system as a retarded one and employ the variation of constants formula for the mean-square exponential ultimate boundedness analysis. Under the assumption that the upper bound of the 6th moment of the estimation error is a known arbitrarily large constant L, explicit conditions in terms of simple scalar inequalities depending on the bound L, tuning parameters and the intensity of measurement noise are established to guarantee the mean-square exponential ultimate boundedness of the ES control systems. Comparatively to the existing results for ES with measurement noise via the qualitative analysis, our approach can provide a quantitative analysis and simplify the stability analysis process as well. A numerical simulation is given to illustrate the efficiency of the proposed method.

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

Publication series

ISSN (Electronic)2405-8963


Conference22nd IFAC World Congress


  • Averaging
  • Extremum seeking
  • Mean-square ultimate boundedness
  • Measurement noise


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