A Multivariable Newton-Based Stochastic Extremum Seeking Control for Systems with Distinct Input Delays

A Multivariable Newton-Based Stochastic Extremum Seeking Control for Systems with Distinct Input Delays | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A Multivariable Newton-Based Stochastic Extremum Seeking Control for Systems with Distinct Input Delays Paulo Cesar Souza Silva, Paulo Cesar Pellanda, Tiago Roux Oliveira This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5427286/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper introduces a novel multivariable Newton-based stochastic extremum-seeking control method for real-time optimization in multi-input systems with distinct input delays. The proposed approach integrates predictor-based feedback and Hessian inverse estimation, achieved through stochastic sinusoidal perturbations, to allow delay compensation while ensuring user-defined convergence rates. This method preserves exponential stability and guarantees convergence to a small neighborhood around the unknown extremum point, even under arbitrarily long delays in actuator channels. The control scheme is further extended to accommodate multi-input, single-output maps with cross-coupled channels, thereby addressing complex, delayed interactions that frequently arise in real-world control systems. Stability analysis is rigorously derived using backstepping transformations and infinite-dimensional averaging techniques, establishing a strong theoretical foundation for robust performance in dynamic settings. Numerical simulations illustrate the proposed method’s effectiveness in delay compensation, highlighting both the challenges and the benefits of managing time-delayed channels in real-time optimization. Systems Engineering Applied Mathematics Electrical Engineering Stochastic systems Input delays Predictor feedback Multivariable extremum seeking Newton algorithm Backstepping %transformation Averaging theory Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5427286","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":376300173,"identity":"8ada439e-b592-40bb-8946-7c48f275f932","order_by":0,"name":"Paulo Cesar Souza Silva","email":"","orcid":"https://orcid.org/0000-0003-0973-7423","institution":"Military Institute of Engineering (IME)","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Paulo","middleName":"Cesar Souza","lastName":"Silva","suffix":""},{"id":376300174,"identity":"489c4371-ad49-4844-9798-586204f2b719","order_by":1,"name":"Paulo Cesar Pellanda","email":"","orcid":"https://orcid.org/0000-0002-4505-2838","institution":"Military Institute of Engineering (IME)","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Paulo","middleName":"Cesar","lastName":"Pellanda","suffix":""},{"id":376300175,"identity":"4dbed069-64ab-4849-8e0b-64d0cd934dbd","order_by":2,"name":"Tiago Roux Oliveira","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAx0lEQVRIiWNgGAWjYDACZhiDvQFI8DAkENTBA9fCc4BYLXCWBEQxYS327MyPX3zcY5O44eYbw8cVMgx55g0EHcZmZjnjWVrizNk5xoZneBiKZQ4Q1MJgZsxz4HBiv3SOmWQDD0PiDEIO42Fm/wbW0iZ5xvwnkVp4jB+DbZHgMWMkTsthnjLGGQfSjGf2pBUDHSZRLEFIC3v/8c0fPhywkd1w/PDGj409NnkEtQABG0IRYw8xGoBJ5gOC/YMoHaNgFIyCUTDCAACq2znSuPwdawAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-2232-8715","institution":"State University of Rio de Janeiro (UERJ)","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Tiago","middleName":"Roux","lastName":"Oliveira","suffix":""}],"badges":[],"createdAt":"2024-11-10 18:33:21","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false,"coiExplicitlySet":false},"doi":"10.21203/rs.3.rs-5427286/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5427286/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":68876148,"identity":"599be2cd-2d62-421e-be6a-5d9c8192a435","added_by":"auto","created_at":"2024-11-13 04:44:54","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":857194,"visible":true,"origin":"","legend":"","description":"","filename":"IJDC2024.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5427286/v1_covered_c6b1e1e4-bbad-4eaa-9271-be819abc0114.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eA Multivariable Newton-Based Stochastic Extremum Seeking Control for Systems with Distinct Input Delays\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Stochastic systems, Input delays, Predictor feedback, Multivariable extremum seeking, Newton algorithm, Backstepping %transformation, Averaging theory","lastPublishedDoi":"10.21203/rs.3.rs-5427286/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5427286/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper introduces a novel multivariable Newton-based stochastic extremum-seeking control method for real-time optimization in multi-input systems with distinct input delays. The proposed approach integrates predictor-based feedback and Hessian inverse estimation, achieved through stochastic sinusoidal perturbations, to allow delay compensation while ensuring user-defined convergence rates. This method preserves exponential stability and guarantees convergence to a small neighborhood around the unknown extremum point, even under arbitrarily long delays in actuator channels. The control scheme is further extended to accommodate multi-input, single-output maps with cross-coupled channels, thereby addressing complex, delayed interactions that frequently arise in real-world control systems. Stability analysis is rigorously derived using backstepping transformations and infinite-dimensional averaging techniques, establishing a strong theoretical foundation for robust performance in dynamic settings. 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