Extremum Seeking for Single-Variable Static Map with Measurement Noise via A Time-Delay Approach

Bowen Zhao, Xuefei Yang*, Emilia Fridman, Bin Zhou

*Corresponding author for this work

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

Abstract

In this article, we introduce a time-delay approach to extremum seeking (ES) for scalar static quadratic maps with measurement noise. The approach involves transforming the ES system into a time-delay neutral type system with stochastic perturbations, which guarantees the stability of the original ES system. Using a Lyapunov-Krasovskii (L-K) method, explicit conditions are established for the mean-square ultimate boundedness of the ES control systems. These conditions are expressed in terms of LMIs and depend on the intensity of measurement noise, tuning parameters, and a known arbitrarily large constant L that bounds the 6th moment of the estimation error. Compared to existing results for ES with measurement noise obtained via qualitative analysis, our approach provides a quantitative analysis via a time-delay approach to averaging. A numerical example is provided to illustrate the efficiency of the proposed method.

Original languageEnglish
Title of host publicationProceedings of 13th IEEE International Conference on CYBER Technology in Automation, Control, and Intelligent Systems, CYBER 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages13-18
Number of pages6
ISBN (Electronic)9798350315196
DOIs
StatePublished - 2023
Event13th IEEE International Conference on CYBER Technology in Automation, Control, and Intelligent Systems, CYBER 2023 - Qinhuangdao, China
Duration: 11 Jul 202314 Jul 2023

Publication series

NameProceedings of 13th IEEE International Conference on CYBER Technology in Automation, Control, and Intelligent Systems, CYBER 2023

Conference

Conference13th IEEE International Conference on CYBER Technology in Automation, Control, and Intelligent Systems, CYBER 2023
Country/TerritoryChina
CityQinhuangdao
Period11/07/2314/07/23

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