Identification of Multivariable Hammerstein Systems with Hysteresis Nonlinearities

Identification of Multivariable Hammerstein Systems with Hysteresis Nonlinearities | 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 Identification of Multivariable Hammerstein Systems with Hysteresis Nonlinearities Luís Henrique Santos, Rodrigo Augusto Ricco, Bruno Otávio Soares Teixeira This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8088269/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 9 You are reading this latest preprint version Abstract This paper addresses the problem of identification of multivariable systems exhibiting hysteresis through the application of the Hammerstein model. The Hammerstein model consists of a generalized rate-dependent Prandtl-Ishlinskii hysteresis block followed by a linear dynamic representation in state space, with both components being multivariable. Building on this framework, we develop a novel identification methodology that integrates a modified version of a particle swarm optimization algorithm, extended to handle multivariable scenarios, along with a subspace algorithm based on harmonic signals. The proposed methodology is tested on two numerical examples. The results suggest that our method is capable to identify models that effectively capture asymmetric hysteresis in coupled, non-minimal phase multivariable systems, even under conditions of white measurement noise. Hysteresis Multivariable Hammerstein models Prandtl-Ishlinskii models State-space models Modified PSO Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 15 Apr, 2026 Reviews received at journal 08 Mar, 2026 Reviews received at journal 20 Feb, 2026 Reviewers agreed at journal 16 Feb, 2026 Reviewers agreed at journal 16 Feb, 2026 Reviewers invited by journal 02 Feb, 2026 Editor assigned by journal 23 Nov, 2025 Submission checks completed at journal 19 Nov, 2025 First submitted to journal 11 Nov, 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. 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. 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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-8088269","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":584481666,"identity":"5f4dabd2-0484-4ef0-b685-7863115ee426","order_by":0,"name":"Luís Henrique Santos","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAr0lEQVRIiWNgGAWjYBACPgbGBhCSY2A+wABiEAZsUC3GDGwJRGthAKtMbCBei0Ry8wfGHXXpG45xJ79g3HGPGC2JbRKMZw7nbjjGu82C8UwxcVqY/7YdyN1wv3ebAWNbAlFagA5rq0s3ANpCtJYGCcY25gSgls0PiNPC8xDol7bDhjOBtjAkniFCCz97+mOQw+T5gLZ8+LiDCC2ojiRRAwMD8wdSdYyCUTAKRsHIAABYnjke9ahBxQAAAABJRU5ErkJggg==","orcid":"","institution":"Universidade Federal de Minas Gerais","correspondingAuthor":true,"prefix":"","firstName":"Luís","middleName":"Henrique","lastName":"Santos","suffix":""},{"id":584481667,"identity":"1c83af29-7b79-4463-99e8-a4c9f8a494b9","order_by":1,"name":"Rodrigo Augusto Ricco","email":"","orcid":"","institution":"Universidade Federal de Ouro Preto","correspondingAuthor":false,"prefix":"","firstName":"Rodrigo","middleName":"Augusto","lastName":"Ricco","suffix":""},{"id":584481668,"identity":"3014e41c-1aa2-4fb6-9174-bbbcc65066d9","order_by":2,"name":"Bruno Otávio Soares Teixeira","email":"","orcid":"","institution":"Universidade Federal de Minas Gerais","correspondingAuthor":false,"prefix":"","firstName":"Bruno","middleName":"Otávio Soares","lastName":"Teixeira","suffix":""}],"badges":[],"createdAt":"2025-11-11 15:09:03","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8088269/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8088269/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101881004,"identity":"150e65cc-9cdc-4abd-bc48-fb58c675f555","added_by":"auto","created_at":"2026-02-04 15:08:52","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2885720,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8088269/v1_covered_36bf071c-0243-4711-9b35-471a1a1c32f0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Identification of Multivariable Hammerstein Systems with Hysteresis Nonlinearities","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":"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":"Hysteresis, Multivariable Hammerstein models, Prandtl-Ishlinskii models, State-space models, Modified PSO","lastPublishedDoi":"10.21203/rs.3.rs-8088269/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8088269/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper addresses the problem of identification of multivariable systems exhibiting hysteresis through the application of the Hammerstein model. 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