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Automatic computation of conservation laws in the calculus of variations and optimal control

2005Journal article Open access
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dc.contributor.authorGouveia, Paulo D.F.
dc.contributor.authorTorres, Delfim F.M.
dc.date.accessioned2010-01-29T19:14:38Z
dc.date.available2010-01-29T19:14:38Z
dc.date.issued2005
dc.description.abstractWe present analytical computational tools that permit us to identify, in an automatic way, conservation laws in optimal control. The central result we use is the famous Noether's theorem, a classical theory developed by Emmy Noether in 1918, in the context of the calculus of variations and mathematical physics, which was extended recently to the more general context of optimal control. We show how a Computer Algebra System can be very helpful in ¯nding the symmetries and corresponding conservation laws in optimal control theory, thus making useful in practice the theoretical results recently obtained in the literature. A Maple implementation is provided and several illustrative examples are given.pt
dc.description.sponsorshipPG was supported by the program PRODEP III/5.3/2003. DT acknowledges the support from the control theory group (cotg) of the R&D unit CEOC, and the project “Advances in Nonlinear Control and Calculus of Variations” POCTI/MAT/41683/2001. The authors are grateful to E. M. Rocha for stimulating discussions.
dc.identifier.citationGouveia, Paulo D.F.; Torres, Delfim F.M. (2005). Automatic computation of conservation laws in the calculus of variations and optimal control. Computational Methods in Applied Mathematics. ISSN 1609-9389. 5:4 p. 387-409pt
dc.identifier.issn1609-9389
dc.identifier.urihttp://hdl.handle.net/10198/1573
dc.language.isoengpt
dc.relationAdvances in Nonlinear Control and Calculus of Variations
dc.relation.publisherversion5(4)pt
dc.subjectOptimal controlpt
dc.subjectCalculus of variationspt
dc.subjectComputer algebrapt
dc.subjectNoether's theorempt
dc.subjectSymmetriespt
dc.subjectConservation lawspt
dc.titleAutomatic computation of conservation laws in the calculus of variations and optimal controlpt
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleAdvances in Nonlinear Control and Calculus of Variations
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/POCI/POCTI%2FMAT%2F41683%2F2001/PT
oaire.citation.endPage409pt
oaire.citation.startPage387pt
oaire.citation.titleComputational Methods in Applied Mathematicspt
oaire.fundingStreamPOCI
person.familyNameGouveia
person.givenNamePaulo D.F.
person.identifier.orcid0000-0003-3049-6230
person.identifier.scopus-author-id20433578000
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccesspt
rcaap.typearticlept
relation.isAuthorOfPublication41c37437-90c4-4e40-893b-44fe4ae1f159
relation.isAuthorOfPublication.latestForDiscovery41c37437-90c4-4e40-893b-44fe4ae1f159
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relation.isProjectOfPublication.latestForDiscoverya6ece8ac-c2bf-4535-9240-5b92d0c7d6e8

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