Direct Robust Adaptive Tracking Control of Electric Vehicles Based on Radial Basis Function Neural Networks

Direct Robust Adaptive Tracking Control of Electric Vehicles Based on Radial Basis Function Neural Networks | 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 Direct Robust Adaptive Tracking Control of Electric Vehicles Based on Radial Basis Function Neural Networks Xiaofang Xiao, Xinxiang Fang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8867541/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 12 You are reading this latest preprint version Abstract This paper proposes a direct robust adaptive tracking control scheme for the longitudinal motion of electric vehicles (EVs) subject to parametric uncertainties, nonlinear dynamics, and external disturbances. The vehicle's longitudinal dynamics are formulated as a second-order nonlinear system with unknown nonlinearities. Instead of identifying the system's unknown functions separately, a radial basis function neural network (RBFNN) is employed to directly approximate the ideal feedback control law, which is derived based on a sliding mode framework and Lyapunov synthesis. To enhance robustness against approximation errors and bounded disturbances, a robust adaptive law incorporating $\sigma$-modification is designed for updating the neural network weights online. The stability of the closed-loop control system is rigorously proved via Lyapunov theory, demonstrating that all signals remain uniformly ultimately bounded (UUB) and the tracking error converges to a small residual set around zero. The controller's performance is independent of the exact knowledge of the vehicle's nonlinear dynamics. Simulation results on a high-fidelity EV model confirm the effectiveness of the proposed controller in achieving accurate velocity tracking under various driving conditions and disturbances. Physical sciences/Engineering Physical sciences/Mathematics and computing Electric vehicles Longitudinal motion control Radial basis function neural network Robust adaptive control Sliding mode control Full Text Additional Declarations No competing interests reported. Supplementary Files Maincode.pdf Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 10 Mar, 2026 Reviews received at journal 09 Mar, 2026 Reviews received at journal 25 Feb, 2026 Reviewers agreed at journal 24 Feb, 2026 Reviewers agreed at journal 24 Feb, 2026 Reviewers agreed at journal 21 Feb, 2026 Reviewers agreed at journal 19 Feb, 2026 Reviewers invited by journal 19 Feb, 2026 Editor invited by journal 17 Feb, 2026 Editor assigned by journal 13 Feb, 2026 Submission checks completed at journal 13 Feb, 2026 First submitted to journal 12 Feb, 2026 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-8867541","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":595085713,"identity":"eeb7916a-8ffa-4c56-94bc-2df30fa7ef2d","order_by":0,"name":"Xiaofang Xiao","email":"","orcid":"","institution":"Hunan Mechanical and Electrical Polytechnic","correspondingAuthor":false,"prefix":"","firstName":"Xiaofang","middleName":"","lastName":"Xiao","suffix":""},{"id":595085715,"identity":"15ffedc2-d442-46cd-a5c2-92509a9ebed6","order_by":1,"name":"Xinxiang Fang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIie3PIQsCMRTA8clgVwarE8TPMDgYNr/KG4JpiiDIBYNBzqB+l7PZPBBM02w8ixguaLPpM1ruFgX3D48X3m8wQkKhHyya4YDk1cbZKCCZ1hOe4ygcjZFQVbiDH2lcUmqQsOZlTj1IdNzfTMpARFYnZsaIWCyhmvBhvwMnPmyuSn022xaR7phVki6xWsFEjtXZInGMKDmoJlyUSJgyOyQjk1IPIm1cQAomk1YTT1JqAi6PpbuOJbgDr/0LFzZ+PJO8LRa9DS5TXNbVBGPy642680/07nMVCoVCf9wbbVxLRwskuaoAAAAASUVORK5CYII=","orcid":"","institution":"Hunan Mechanical and Electrical Polytechnic","correspondingAuthor":true,"prefix":"","firstName":"Xinxiang","middleName":"","lastName":"Fang","suffix":""}],"badges":[],"createdAt":"2026-02-13 05:08:57","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8867541/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8867541/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103506054,"identity":"91e26691-06c4-404a-9892-742995e76c3e","added_by":"auto","created_at":"2026-02-26 13:33:56","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1966084,"visible":true,"origin":"","legend":"","description":"","filename":"ScientificReports0213.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8867541/v1_covered_9e8a65c0-7536-4377-b41b-c18e3af32786.pdf"},{"id":103349795,"identity":"4a2862f9-ec2d-4e8d-9b6f-12182fbc8ea9","added_by":"auto","created_at":"2026-02-24 16:48:28","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":137040,"visible":true,"origin":"","legend":"","description":"","filename":"Maincode.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8867541/v1/dd0e246da84af95b68312209.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Direct Robust Adaptive Tracking Control of Electric Vehicles Based on Radial Basis Function Neural Networks","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"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":"Electric vehicles, Longitudinal motion control, Radial basis function neural network, Robust adaptive control, Sliding mode control","lastPublishedDoi":"10.21203/rs.3.rs-8867541/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8867541/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper proposes a direct robust adaptive tracking control scheme for the longitudinal motion of electric vehicles (EVs) subject to parametric uncertainties, nonlinear dynamics, and external disturbances. The vehicle's longitudinal dynamics are formulated as a second-order nonlinear system with unknown nonlinearities. Instead of identifying the system's unknown functions separately, a radial basis function neural network (RBFNN) is employed to directly approximate the ideal feedback control law, which is derived based on a sliding mode framework and Lyapunov synthesis. To enhance robustness against approximation errors and bounded disturbances, a robust adaptive law incorporating $\\sigma$-modification is designed for updating the neural network weights online. The stability of the closed-loop control system is rigorously proved via Lyapunov theory, demonstrating that all signals remain uniformly ultimately bounded (UUB) and the tracking error converges to a small residual set around zero. The controller's performance is independent of the exact knowledge of the vehicle's nonlinear dynamics. 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