Experience-based Integral Reinforcement Learning Consensus for Nonlinear Multi-agent Systems

Experience-based Integral Reinforcement Learning Consensus for Nonlinear Multi-agent Systems | 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 Article Experience-based Integral Reinforcement Learning Consensus for Nonlinear Multi-agent Systems Longquan Ma, Huarong Zhao, Yuhao Chen, Yi Gao, Hongnian Yu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5811620/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 26 Sep, 2025 Read the published version in Scientific Reports → Version 1 posted 14 You are reading this latest preprint version Abstract This paper investigates an optimal consensus control problem and proposes a policy iteration algorithm based on online integral reinforcement learning for nonlinear multi-agent systems with unknown dynamics. Introducing a critic and actor networks into the traditional policy iteration avoids the identification of unknown dynamics. To address the issue of local optima in online learning, an experience-based weight-tuning law is introduced to ensure the persistence of excitation conditions during the training phase. The theoretical results show that the system is asymptotically stable, and the network weights converge. Finally, the effectiveness and correctness have been verified by several simulation studies. Physical sciences/Energy science and technology/Energy harvesting Physical sciences/Energy science and technology/Energy storage Physical sciences/Energy science and technology/Renewable energy Physical sciences/Mathematics and computing/Applied mathematics Physical sciences/Mathematics and computing/Information technology Physical sciences/Physics/Applied physics Physical sciences/Physics/Electronics photonics and device physics Physical sciences/Physics/Information theory and computation Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 26 Sep, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 02 Jun, 2025 Reviews received at journal 13 May, 2025 Reviews received at journal 07 May, 2025 Reviewers agreed at journal 05 May, 2025 Reviews received at journal 03 May, 2025 Reviewers agreed at journal 03 May, 2025 Reviews received at journal 02 May, 2025 Reviewers agreed at journal 22 Apr, 2025 Reviews received at journal 22 Apr, 2025 Reviewers agreed at journal 22 Apr, 2025 Reviewers agreed at journal 22 Apr, 2025 Reviewers invited by journal 22 Apr, 2025 Submission checks completed at journal 16 Apr, 2025 First submitted to journal 02 Apr, 2025 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. 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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-5811620","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":446478008,"identity":"e3c7f654-8654-4075-9adf-c30345e331ef","order_by":0,"name":"Longquan Ma","email":"","orcid":"","institution":"Jiangnan University","correspondingAuthor":false,"prefix":"","firstName":"Longquan","middleName":"","lastName":"Ma","suffix":""},{"id":446478009,"identity":"105ae1c5-7c25-49b6-a00a-ca3d4744d210","order_by":1,"name":"Huarong Zhao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8ElEQVRIiWNgGAWjYBACAwYGNiBlw8yGEEsgSksa6VoOI4sR0GIuffzZgx8V59n52M8efl1Qc4eBnz3HgOHnDtxaLPsS0g17ztxmZuPJS7OecewZg2TPGwPG3jN4HHaG4ZgEbxtQC0OOmTEP22EGgxs5BsyMbfi0MLZJ/m07x8zG/wao5d9hBnvCWpjZpHnbDjCzSeQYP+ZtA9oiQVALG5u0zJlkoJY3Zsy8fYd5JM48KzjYi1cL+zPJNxV2yfL9Ocafeb4dluNvT9744CceLTCQDMRsEkCCB8Q7QFgDA4MdEDN/IEblKBgFo2AUjDwAABVSSNMVD05hAAAAAElFTkSuQmCC","orcid":"","institution":"Jiangnan University","correspondingAuthor":true,"prefix":"","firstName":"Huarong","middleName":"","lastName":"Zhao","suffix":""},{"id":446478010,"identity":"1c536858-681e-4a68-b9a1-589abe0c1a2b","order_by":2,"name":"Yuhao Chen","email":"","orcid":"","institution":"Jiangnan University","correspondingAuthor":false,"prefix":"","firstName":"Yuhao","middleName":"","lastName":"Chen","suffix":""},{"id":446478011,"identity":"396f656b-4fdc-4545-ab2e-2be93d13bf7a","order_by":3,"name":"Yi Gao","email":"","orcid":"","institution":"Wuxi Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Yi","middleName":"","lastName":"Gao","suffix":""},{"id":446478012,"identity":"4bbe2f8b-521c-4401-9eb0-91c541e666f7","order_by":4,"name":"Hongnian Yu","email":"","orcid":"","institution":"Edinburgh Napier University","correspondingAuthor":false,"prefix":"","firstName":"Hongnian","middleName":"","lastName":"Yu","suffix":""}],"badges":[],"createdAt":"2025-01-12 02:53:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5811620/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5811620/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-15573-w","type":"published","date":"2025-09-26T15:57:26+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":92430454,"identity":"f4a56603-152a-48fc-886b-1d66b6e841f5","added_by":"auto","created_at":"2025-09-29 16:04:53","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2043377,"visible":true,"origin":"","legend":"","description":"","filename":"ScientificReports2025resubmmited.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5811620/v1_covered_c934ffdf-8499-4fba-bc23-99f74ce3504e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Experience-based Integral Reinforcement Learning Consensus for Nonlinear Multi-agent Systems","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-5811620/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5811620/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper investigates an optimal consensus control problem and proposes a policy iteration algorithm based on online integral reinforcement learning for nonlinear multi-agent systems with unknown dynamics. 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