Multiple extended state observers with second-level adaptation: a convex combination framework for low-peaking state estimation

Multiple extended state observers with second-level adaptation: a convex combination framework for low-peaking state estimation | 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 Multiple extended state observers with second-level adaptation: a convex combination framework for low-peaking state estimation Huahua Liu, Dongyang Qu, Qing Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6527958/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 proposes a novel design framework for multiple extended state observers(MESOs) that utilizes second-level adaptation techniques to enhance the transient response and mitigate undesirable peaking phenomenon associated with extended state observers. The proposed method treats state estimation as a convex combination of the information obtained from multiple extended state observers. In this regard, it is demonstrated that certain constant parameters exist within this combination, leading to precise state estimation; then, these parameters are estimated using an adaptive algorithm. The convergence of state estimation to the state of the plant is proved. Moreover, compared to a single extended state observer, MESO is proved to provide state estimates with significantly smaller peaking. Simulation results demonstrate that MESO can provide accurate state estimates with arbitrary low peaking. Extended state observer Uncertain nonlinear systems Peaking phenomenon Second-level adaptation 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-6527958","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":451057002,"identity":"d9413091-6681-4892-9f13-a7e9bd898d4b","order_by":0,"name":"Huahua Liu","email":"","orcid":"","institution":"Beihang University","correspondingAuthor":false,"prefix":"","firstName":"Huahua","middleName":"","lastName":"Liu","suffix":""},{"id":451057003,"identity":"4b095fc6-a893-4738-bd05-ef461fc56c4b","order_by":1,"name":"Dongyang Qu","email":"","orcid":"","institution":"Beihang University","correspondingAuthor":false,"prefix":"","firstName":"Dongyang","middleName":"","lastName":"Qu","suffix":""},{"id":451057004,"identity":"f955cab2-4ec9-401d-9f2f-e3b43cbdd8c5","order_by":2,"name":"Qing Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5klEQVRIiWNgGAWjYNACAwYGfgkIk7GBaC2SM0jTAtJ1g1gtBsfPHn7xpuCO3ebbPYYffjDYyG44wPzsAV4tZ/LSLOcYPEvedueMsWQPQ5rxhgNs5gb4tJgdyDEz5jE4nGx2I8dAgofhcOKGAzxsEni1nH8D0WI8I8f45x+G/0RouZFj/Bioxc5AIsdMmofhAGEt9jfemDHOMTicIHHnWJm1jEGy8czDbGZ4tUj25xh/ePPnsD3/7ObNN99U2Mn2HW9+hlcLELABfc2Q2ABmg4KKmYB6kJIPQC32hNWNglEwCkbBiAUAbH9MsChzAY0AAAAASUVORK5CYII=","orcid":"","institution":"Beihang University","correspondingAuthor":true,"prefix":"","firstName":"Qing","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2025-04-25 10:23:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6527958/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6527958/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":83412346,"identity":"bf11c463-b903-48b2-91db-b8cf757e614f","added_by":"auto","created_at":"2025-05-25 15:46:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5853769,"visible":true,"origin":"","legend":"","description":"","filename":"Multipleextendedstateobserverswithsecondleveladaptationaconvexcombinationframeworkforlowpeakingstateestimation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6527958/v1_covered_061d73d2-0b72-44bf-80d1-35ea1a857262.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Multiple extended state observers with second-level adaptation: a convex combination framework for low-peaking state estimation","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":"Extended state observer, Uncertain nonlinear systems, Peaking phenomenon, Second-level adaptation","lastPublishedDoi":"10.21203/rs.3.rs-6527958/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6527958/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper proposes a novel design framework for multiple extended state observers(MESOs) that utilizes second-level adaptation techniques to enhance the transient response and mitigate undesirable peaking phenomenon associated with extended state observers. 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