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

Detalhes bibliográficos
Autor(a) principal: Gouveia, Paulo D.F.
Data de Publicação: 2005
Outros Autores: Torres, Delfim F.M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10198/1573
Resumo: We 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.
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spelling Automatic computation of conservation laws in the calculus of variations and optimal controlOptimal controlCalculus of variationsComputer algebraNoether's theoremSymmetriesConservation lawsWe 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.PG 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.Biblioteca Digital do IPBGouveia, Paulo D.F.Torres, Delfim F.M.2010-01-29T19:14:38Z20052005-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10198/1573engGouveia, 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. 387-4091609-9389info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-21T10:05:50Zoai:bibliotecadigital.ipb.pt:10198/1573Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:55:10.727339Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Automatic computation of conservation laws in the calculus of variations and optimal control
title Automatic computation of conservation laws in the calculus of variations and optimal control
spellingShingle Automatic computation of conservation laws in the calculus of variations and optimal control
Gouveia, Paulo D.F.
Optimal control
Calculus of variations
Computer algebra
Noether's theorem
Symmetries
Conservation laws
title_short Automatic computation of conservation laws in the calculus of variations and optimal control
title_full Automatic computation of conservation laws in the calculus of variations and optimal control
title_fullStr Automatic computation of conservation laws in the calculus of variations and optimal control
title_full_unstemmed Automatic computation of conservation laws in the calculus of variations and optimal control
title_sort Automatic computation of conservation laws in the calculus of variations and optimal control
author Gouveia, Paulo D.F.
author_facet Gouveia, Paulo D.F.
Torres, Delfim F.M.
author_role author
author2 Torres, Delfim F.M.
author2_role author
dc.contributor.none.fl_str_mv Biblioteca Digital do IPB
dc.contributor.author.fl_str_mv Gouveia, Paulo D.F.
Torres, Delfim F.M.
dc.subject.por.fl_str_mv Optimal control
Calculus of variations
Computer algebra
Noether's theorem
Symmetries
Conservation laws
topic Optimal control
Calculus of variations
Computer algebra
Noether's theorem
Symmetries
Conservation laws
description We 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.
publishDate 2005
dc.date.none.fl_str_mv 2005
2005-01-01T00:00:00Z
2010-01-29T19:14:38Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10198/1573
url http://hdl.handle.net/10198/1573
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Gouveia, 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. 387-409
1609-9389
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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