Safety-Critical Distributed Optimization with Input Constraints and Unknown Second-Order Dynamics

Safety-Critical Distributed Optimization with Input Constraints and Unknown Second-Order Dynamics | 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 Safety-Critical Distributed Optimization with Input Constraints and Unknown Second-Order Dynamics Jing Xie, Fei Chen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6191237/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 investigates the distributed safe optimization problem for uncertain second-order nonlinear multi-agent systems subject to inequality and input constraints. The primary goal is to collaboratively minimize the sum of local objective functions, with agents having access only to their own local information and the states of neighboring agents. To address this challenge, we introduce a desired distributed optimization algorithm that incorporates a Control Lyapunov Function (CLF) based condition. For handling inequality and input constraints, a high-order Control Barrier Function (CBF) based method is utilized. Additionally, quadratic programming is employed to determine the control inputs. When the desired optimization trajectory conflicts with the constraints, a relaxed CLF-based condition is adopted. The practical applicability of the theoretical findings is demonstrated through a series of numerical examples. Control barrier function Distributed optimization Input constraint Unkown second-order dynamics Full Text Additional Declarations No competing interests reported. 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-6191237","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":429538275,"identity":"a113d7ca-3a64-4797-b12d-df7ec93571ad","order_by":0,"name":"Jing Xie","email":"","orcid":"","institution":"Northeastern University","correspondingAuthor":false,"prefix":"","firstName":"Jing","middleName":"","lastName":"Xie","suffix":""},{"id":429538279,"identity":"52fe83f4-4efe-44ac-9a54-77065083e194","order_by":1,"name":"Fei Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIiWNgGAWjYBAC9gYeIFkBxED6AAMDM2EtPAdAWs6QrIWxDaKFgTgt7GcPPi6cd0fenOfwwwMMFdaJDexnD+DXwpOXbDxz2zPDnb1tBgcYzqQnNvDkJeDVYi/BYybNu+0w44bzDAYHGNsOJzZI8Bjgt0WCx/w375zD9hvOs384wPiPOC1mzLwNhxM3nO0B2tJAjBaeHGNpnmOHkzecOVNwIOFYunEbTw4BLexnDD/z1By23XAmffOHDzXWsv3sZ/BrQQUJQMxGgvpRMApGwSgYBTgAAGYTRTE5BY7BAAAAAElFTkSuQmCC","orcid":"","institution":"Nankai University","correspondingAuthor":true,"prefix":"","firstName":"Fei","middleName":"","lastName":"Chen","suffix":""}],"badges":[],"createdAt":"2025-03-10 02:53:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6191237/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6191237/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":93561932,"identity":"0b79998b-d640-4a52-a797-638d0714d0b5","added_by":"auto","created_at":"2025-10-15 07:47:19","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2414009,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6191237/v1_covered_eca6bc58-db12-4de1-9478-b96bff883ef2.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Safety-Critical Distributed Optimization with Input Constraints and Unknown Second-Order Dynamics","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"Control barrier function, Distributed optimization, Input constraint, Unkown second-order dynamics","lastPublishedDoi":"10.21203/rs.3.rs-6191237/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6191237/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper investigates the distributed safe optimization problem for uncertain second-order nonlinear multi-agent systems subject to inequality and input constraints. 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