Bias compensation based recursive least squares identification algorithm for multivariable Hammerstein nonlinear systems

Bias compensation based recursive least squares identification algorithm for multivariable Hammerstein nonlinear systems | 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 Bias compensation based recursive least squares identification algorithm for multivariable Hammerstein nonlinear systems Bensheng Lyu, Qiang Wang, Yanling Xu, Huajun Zhang, Chunbo Cai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4629131/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 The multivariable Hammerstein nonlinear system contains the sum of bilinear parameters, which is not a regression form. By using the special properties of binary signals, we can transform the sum of bilinear parameter matrices into two different models, achieving the parameter separation for parallel nonlinear subsystems and a linear subsystem. In order to improve the accuracy of parameter identification, this paper uses a biased correction technique to compensate a biased recursive least squares estimates. Then, a bias compensation based recursive least squares algorithm is proposed to separately identify the parameters of a linear subsystem and parallel nonlinear systems. The numerical simulation indicate that the proposed algorithm has a higher accuracy than recursive least squares and over-parametrization based identification algorithms. The multivariate Hammerstein nonlinear system is implemented on a case study from the process industry namely the continuous stirred tank reactor. The accuracy of the prediction is improved by a biased correction term. multivariable system Hammerstein system bias compensation recursive least squares algorithm parameter estimation 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-4629131","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":323495187,"identity":"fc2e3c3b-959d-447c-8727-5ffff48aa5e4","order_by":0,"name":"Bensheng Lyu","email":"","orcid":"","institution":"Shanghai Jiao Tong University","correspondingAuthor":false,"prefix":"","firstName":"Bensheng","middleName":"","lastName":"Lyu","suffix":""},{"id":323495189,"identity":"e8280ee8-f5ae-40eb-9616-a299585635d4","order_by":1,"name":"Qiang Wang","email":"","orcid":"","institution":"Shanghai Jiao Tong University","correspondingAuthor":false,"prefix":"","firstName":"Qiang","middleName":"","lastName":"Wang","suffix":""},{"id":323495191,"identity":"a3ff84ee-b623-4668-8600-199c0948f6ad","order_by":2,"name":"Yanling Xu","email":"","orcid":"","institution":"Shanghai Jiao Tong University","correspondingAuthor":false,"prefix":"","firstName":"Yanling","middleName":"","lastName":"Xu","suffix":""},{"id":323495193,"identity":"9316c89d-016d-45ce-b4b1-6dcbf7728c71","order_by":3,"name":"Huajun Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBElEQVRIiWNgGAWjYDACCSBmbABjxgcMPGAxA6K1MBsw8BiQoAUI2CSgqvFrkZ/d/Ozh1x2H5Zln5B6r/CHzJ7GBvXmbBEPNHZxaGOccMzeWPXPYsHFGXtptHh6DxAaeY2USDMee4dTCLJFgJi3ZdpixcUaO2W0GkBaJHDMJxobDOLWwSaR/A2mxB2kp/AHSIv8GvxYeoJmSH9sOJ4K0MIAdJsGDX4uERE6ZNGNbenJjzxtjaR4eY+M2nrRii4RjuLXIz0jfJvmzzdp2Y3uO4cefPXKy/eyHN974UINbCzgIQHFu2AAkGHuAvgMJJeDVAFT4A2QdmPmDgNJRMApGwSgYkQAAX0VRWEJyBGIAAAAASUVORK5CYII=","orcid":"","institution":"Shanghai Jiao Tong University","correspondingAuthor":true,"prefix":"","firstName":"Huajun","middleName":"","lastName":"Zhang","suffix":""},{"id":323495196,"identity":"78c1d5eb-8c2c-4c01-b70e-19110b635d4e","order_by":4,"name":"Chunbo Cai","email":"","orcid":"","institution":"Shanghai Maritime University","correspondingAuthor":false,"prefix":"","firstName":"Chunbo","middleName":"","lastName":"Cai","suffix":""}],"badges":[],"createdAt":"2024-06-24 09:39:55","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4629131/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4629131/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":63244871,"identity":"9c872ca7-f374-43df-9b82-473adf87f652","added_by":"auto","created_at":"2024-08-26 05:31:56","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":665206,"visible":true,"origin":"","legend":"","description":"","filename":"BiascompensationbasedrecursiveleastsquaresidentificationalgorithmformultivariableHammerstein.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4629131/v1_covered_d983c83f-03c0-4e7e-8531-c5cbc904e5ad.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Bias compensation based recursive least squares identification algorithm for multivariable Hammerstein nonlinear systems","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":"multivariable system, Hammerstein system, bias compensation, recursive least squares algorithm, parameter estimation","lastPublishedDoi":"10.21203/rs.3.rs-4629131/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4629131/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The multivariable Hammerstein nonlinear system contains the sum of bilinear parameters, which is not a regression form. 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