Adjoint Gradient Computation for an Extremal Value of a System Output

Adjoint Gradient Computation for an Extremal Value of a System Output | 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 Adjoint Gradient Computation for an Extremal Value of a System Output Philipp Zallinger, Daniel Lichtenecker, Philipp Eichmeir, Wolfgang Steiner, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6564907/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 14 Oct, 2025 Read the published version in Multibody System Dynamics → Version 1 posted 9 You are reading this latest preprint version Abstract Extremal values of a system output pose major issues in various disciplines, e.g., the maximum velocity in human-robot collaboration results in high contact forces in the event of a collision, or force and stress peaks cause faster crack growth or fatigue of components. Reducing these extremal values implies a reduction in the risks to humans and an increase in the durability of the components. Therefore, the present paper focuses on minimizing an extremal value of a system output of dynamical system, whereby a gradient-based solution strategy based on the adjoint method is proposed. Since several local extremal values can occur in the time evolution of the system output, it is necessary to apply multi-objective optimization, whereby in particular the largest value is to be minimized. One promising approach in this regard is found in the goal attainment method, which is implemented in the MATLAB function fminimax, or alternatively, the so-called minimax problem can be investigated in a smoothed objective open for any nonlinear programming software package. In the scope of these minimax problems, the maximum reaction force of a one-mass oscillator and the maximum velocity of the tool center point of a two-axis robot during a rest-to-rest maneuver are minimized efficiently using the proposed adjoint gradient. Adjoint gradient method Multi-objective optimization Minimax problems Nonlinear programming Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 14 Oct, 2025 Read the published version in Multibody System Dynamics → Version 1 posted Editorial decision: Revision requested 15 Jul, 2025 Reviews received at journal 04 Jul, 2025 Reviews received at journal 06 Jun, 2025 Reviewers agreed at journal 02 Jun, 2025 Reviewers agreed at journal 18 May, 2025 Reviewers invited by journal 02 May, 2025 Editor assigned by journal 30 Apr, 2025 Submission checks completed at journal 30 Apr, 2025 First submitted to journal 30 Apr, 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. 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-6564907","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":451726453,"identity":"7823be3f-1bcb-4657-b714-1f03a081ab78","order_by":0,"name":"Philipp Zallinger","email":"data:image/png;base64,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","orcid":"","institution":"University of Applied Sciences Upper Austria","correspondingAuthor":true,"prefix":"","firstName":"Philipp","middleName":"","lastName":"Zallinger","suffix":""},{"id":451726454,"identity":"3e97741d-711e-4d44-b34d-b5879141290e","order_by":1,"name":"Daniel Lichtenecker","email":"","orcid":"","institution":"Technical University of Munich","correspondingAuthor":false,"prefix":"","firstName":"Daniel","middleName":"","lastName":"Lichtenecker","suffix":""},{"id":451726455,"identity":"99fc088c-3af8-4501-84fb-b9ee664e8586","order_by":2,"name":"Philipp Eichmeir","email":"","orcid":"","institution":"University of Applied Sciences Upper Austria","correspondingAuthor":false,"prefix":"","firstName":"Philipp","middleName":"","lastName":"Eichmeir","suffix":""},{"id":451726456,"identity":"44956ddc-e2e2-43cd-a7c7-ee56d4d675a5","order_by":3,"name":"Wolfgang Steiner","email":"","orcid":"","institution":"University of Applied Sciences Upper Austria","correspondingAuthor":false,"prefix":"","firstName":"Wolfgang","middleName":"","lastName":"Steiner","suffix":""},{"id":451726457,"identity":"1dbed750-91be-4aea-8023-2f5d5202f223","order_by":4,"name":"Karin Nachbagauer","email":"","orcid":"","institution":"University of Applied Sciences Upper Austria","correspondingAuthor":false,"prefix":"","firstName":"Karin","middleName":"","lastName":"Nachbagauer","suffix":""}],"badges":[],"createdAt":"2025-04-30 12:31:45","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6564907/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6564907/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11044-025-10113-w","type":"published","date":"2025-10-14T15:57:19+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":93955959,"identity":"d88cf23c-dd2e-47a2-93ad-1fcadf69c70d","added_by":"auto","created_at":"2025-10-20 16:08:11","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":420138,"visible":true,"origin":"","legend":"","description":"","filename":"20250430SubmissionlMBDZallinger.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6564907/v1_covered_42bca8a3-3be9-419a-936e-190227f9e95f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Adjoint Gradient Computation for an Extremal Value of a System Output","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"multibody-system-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mubo","sideBox":"Learn more about [Multibody System Dynamics](http://link.springer.com/journal/11044)","snPcode":"11044","submissionUrl":"https://submission.nature.com/new-submission/11044/3","title":"Multibody System Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Adjoint gradient method, Multi-objective optimization, Minimax problems, Nonlinear programming","lastPublishedDoi":"10.21203/rs.3.rs-6564907/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6564907/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Extremal values of a system output pose major issues in various disciplines, e.g., the maximum velocity in human-robot collaboration results in high contact forces in the event of a collision, or force and stress peaks cause faster crack growth or fatigue of components. Reducing these extremal values implies a reduction in the risks to humans and an increase in the durability of the components. Therefore, the present paper focuses on minimizing an extremal value of a system output of dynamical system, whereby a gradient-based solution strategy based on the adjoint method is proposed. Since several local extremal values can occur in the time evolution of the system output, it is necessary to apply multi-objective optimization, whereby in particular the largest value is to be minimized. One promising approach in this regard is found in the goal attainment method, which is implemented in the MATLAB function fminimax, or alternatively, the so-called minimax problem can be investigated in a smoothed objective open for any nonlinear programming software package. In the scope of these minimax problems, the maximum reaction force of a one-mass oscillator and the maximum velocity of the tool center point of a two-axis robot during a rest-to-rest maneuver are minimized efficiently using the proposed adjoint gradient.","manuscriptTitle":"Adjoint Gradient Computation for an Extremal Value of a System Output","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-07 03:51:39","doi":"10.21203/rs.3.rs-6564907/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-07-15T18:55:23+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-04T21:06:04+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-06T14:00:24+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"47473466074401613873844816177331449832","date":"2025-06-02T07:12:49+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"58114232753077614593643274983172931112","date":"2025-05-19T01:16:42+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-05-02T04:50:44+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-04-30T19:58:48+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-04-30T15:01:44+00:00","index":"","fulltext":""},{"type":"submitted","content":"Multibody System Dynamics","date":"2025-04-30T12:19:27+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"multibody-system-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mubo","sideBox":"Learn more about [Multibody System Dynamics](http://link.springer.com/journal/11044)","snPcode":"11044","submissionUrl":"https://submission.nature.com/new-submission/11044/3","title":"Multibody System Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d737ac2d-7c94-433f-94c8-707855c24479","owner":[],"postedDate":"May 7th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-10-20T16:00:35+00:00","versionOfRecord":{"articleIdentity":"rs-6564907","link":"https://doi.org/10.1007/s11044-025-10113-w","journal":{"identity":"multibody-system-dynamics","isVorOnly":false,"title":"Multibody System Dynamics"},"publishedOn":"2025-10-14 15:57:19","publishedOnDateReadable":"October 14th, 2025"},"versionCreatedAt":"2025-05-07 03:51:39","video":"","vorDoi":"10.1007/s11044-025-10113-w","vorDoiUrl":"https://doi.org/10.1007/s11044-025-10113-w","workflowStages":[]},"version":"v1","identity":"rs-6564907","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6564907","identity":"rs-6564907","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}