Event-triggered Optimal Consensus for Discrete-time Nonlinear Multiagent Systems with DoS attacks via Reinforcement Learning Method

Event-triggered Optimal Consensus for Discrete-time Nonlinear Multiagent Systems with DoS attacks via Reinforcement Learning Method | 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 Event-triggered Optimal Consensus for Discrete-time Nonlinear Multiagent Systems with DoS attacks via Reinforcement Learning Method Yujie Liao, Xin Wang, Ziming Wang, Sen Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3855439/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 11 Feb, 2026 Read the published version in Nonlinear Dynamics → Version 1 posted 10 You are reading this latest preprint version Abstract This paper focuses on the event-triggered optimal control problem of discrete-time nonlinear multiagent systems (MASs) via the reinforcement learning method. Distinguished from the existing consensus protocols for discrete-time multiagent systems under the ideal communication scenario, the considered model suffers from input saturation, unknown external disturbance, and denial-of-service (DoS) attacks. According to the approximation capability of the radial basis function neural network(RBF NN), the disturbance network is established to tackle the effect of the unknown disturbance on consensus issues. Subsequently, the composite controller is derived with the reinforcement learning strategy to deal with the DoS attacks, where the update frequency of the actor-critic networks and controllers is determined by the novel event-triggered mechanism. Finally, two simulations are formulated to verify the feasibility of the proposed method. Reinforcement Learning Optimal Control Multiagent Systems DoS Attack. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 11 Feb, 2026 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Revision requested 20 Jun, 2025 Reviews received at journal 12 Feb, 2025 Reviewers agreed at journal 17 Jan, 2025 Reviews received at journal 15 Jun, 2024 Reviewers agreed at journal 30 May, 2024 Reviewers agreed at journal 29 May, 2024 Reviewers invited by journal 22 Jan, 2024 Editor assigned by journal 17 Jan, 2024 Submission checks completed at journal 17 Jan, 2024 First submitted to journal 11 Jan, 2024 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. 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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-3855439","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":267716009,"identity":"81d340c1-5d64-4ffe-a875-52c1e95ea2c7","order_by":0,"name":"Yujie Liao","email":"","orcid":"","institution":"Southwest University","correspondingAuthor":false,"prefix":"","firstName":"Yujie","middleName":"","lastName":"Liao","suffix":""},{"id":267716010,"identity":"ed732986-cb89-4f61-a47c-13da4714b280","order_by":1,"name":"Xin Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzUlEQVRIiWNgGAWjYDACZgTrwIEPP0jTwpZ4cGYPafbxGB/mYCNCncFx3mMSP3fU2hvcyPlwmIGHQZ5f7AB+LZLNfGmSvWeOJ264kbvhcIEFg+HM2Qn4tfAz85jd4G07lmAG0jKDhyHB4DYBLWxALTf/th2zN7uR8+AwDxsRWkC23OZtq2HcdiOHgTgtks085r9l2w4k7j/zzAAYyBKE/WJw/oyx4du2OnvJ9uTHHz78sJHnlyagBQoOwxgSRCkHgTqiVY6CUTAKRsEIBAD0FEXyloOpBgAAAABJRU5ErkJggg==","orcid":"","institution":"Southwest University","correspondingAuthor":true,"prefix":"","firstName":"Xin","middleName":"","lastName":"Wang","suffix":""},{"id":267716011,"identity":"8e807bfe-4175-474b-81db-32361ce2fb95","order_by":2,"name":"Ziming Wang","email":"","orcid":"","institution":"The Hong Kong University of Science and Technology (Guangzhou)","correspondingAuthor":false,"prefix":"","firstName":"Ziming","middleName":"","lastName":"Wang","suffix":""},{"id":267716012,"identity":"28ec1a53-71aa-4a9c-a0c1-bb9c099d1540","order_by":3,"name":"Sen Zhang","email":"","orcid":"","institution":"Southwest University","correspondingAuthor":false,"prefix":"","firstName":"Sen","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2024-01-12 02:59:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3855439/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3855439/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11071-025-12095-y","type":"published","date":"2026-02-11T15:58:51+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":102785372,"identity":"7e460493-bbf1-4f42-a3ec-d7cdf07613bf","added_by":"auto","created_at":"2026-02-16 16:05:49","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":564553,"visible":true,"origin":"","legend":"","description":"","filename":"Document.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3855439/v1_covered_d8107e89-7987-4395-87a6-27a7ac459107.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Event-triggered Optimal Consensus for Discrete-time Nonlinear Multiagent Systems with DoS attacks via Reinforcement Learning Method","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":"nonlinear-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nody","sideBox":"Learn more about [Nonlinear Dynamics](https://www.springer.com/journal/11071)","snPcode":"11071","submissionUrl":"https://submission.nature.com/new-submission/11071/3","title":"Nonlinear Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Reinforcement Learning, Optimal Control, Multiagent Systems, DoS Attack.","lastPublishedDoi":"10.21203/rs.3.rs-3855439/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3855439/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper focuses on the event-triggered optimal control problem of discrete-time nonlinear multiagent systems (MASs) via the reinforcement learning method. 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