Publicação
Automatic computation of conservation laws in the calculus of variations and optimal control
| Resumo: | We present analytic 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, and which was extended recently to the more general context of optimal control. We show how a Computer Algebra System can be very helpful in finding 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 given. |
|---|---|
| Autores principais: | Gouveia, Paulo D.F. |
| Outros Autores: | Torres, Delfim F.M. |
| Assunto: | Optimal control Calculus of variations Computer algebra Noether’s theorem Symmetries Conservation laws |
| Ano: | 2006 |
| País: | Portugal |
| Tipo de documento: | working paper |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade Politécnica de Bragança |
| Idioma: | inglês |
| Origem: | Biblioteca Digital da UPB |
| _version_ | 1877782696211513344 |
|---|---|
| author | Gouveia, Paulo D.F. |
| author2 | Torres, Delfim F.M. |
| author2_role | author |
| author_facet | Gouveia, Paulo D.F. Torres, Delfim F.M. |
| author_role | author |
| contributor_name_str_mv | Biblioteca Digital da UPB |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Gouveia, Paulo D.F.\",\"Person.identifier.orcid\":\"0000-0003-3049-6230\",\"Person.identifier.scopusAuthorID\":\"20433578000\"},{\"Person.name\":\"Torres, Delfim F.M.\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Biblioteca Digital da UPB |
| datacite.creators.creator.creatorName.fl_str_mv | Gouveia, Paulo D.F. Torres, Delfim F.M. |
| datacite.date.Accepted.fl_str_mv | 2006-01-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2010-02-17T17:04:15Z |
| datacite.date.embargoed.fl_str_mv | 2010-02-17T17:04:15Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Optimal control Calculus of variations Computer algebra Noether’s theorem Symmetries Conservation laws |
| datacite.titles.title.fl_str_mv | Automatic computation of conservation laws in the calculus of variations and optimal control |
| dc.contributor.none.fl_str_mv | Biblioteca Digital da UPB |
| dc.creator.none.fl_str_mv | Gouveia, Paulo D.F. Torres, Delfim F.M. |
| dc.date.Accepted.fl_str_mv | 2006-01-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2010-02-17T17:04:15Z |
| dc.date.embargoed.fl_str_mv | 2010-02-17T17:04:15Z |
| dc.format.none.fl_str_mv | application/octet-stream image/tiff |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10198/1970 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Maplesoft |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Optimal control Calculus of variations Computer algebra Noether’s theorem Symmetries Conservation laws |
| dc.title.fl_str_mv | Automatic computation of conservation laws in the calculus of variations and optimal control |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_8042 |
| description | We present analytic 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, and which was extended recently to the more general context of optimal control. We show how a Computer Algebra System can be very helpful in finding 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 given. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | workingPaper |
| fulltext.url.fl_str_mv | https://bibliotecadigital.unipb.pt/bitstreams/3405d3f6-754b-4526-9563-004672bfa6b4/download |
| id | ipb_944f493f1d0d06243f2d371fda154c91 |
| identifier.url.fl_str_mv | http://hdl.handle.net/10198/1970 |
| inst_facet_str | urn:organizationAcronym:unipb{{{_:::_}}}Universidade Politécnica de Bragança |
| instacron_str | unipb |
| institution | Universidade Politécnica de Bragança |
| instname_str | Universidade Politécnica de Bragança |
| language | eng |
| network_acronym_str | ipb |
| network_name_str | Biblioteca Digital da UPB |
| oai_identifier_str | oai:bibliotecadigital.unipb.pt:10198/1970 |
| organization_str_mv | urn:organizationAcronym:unipb |
| person_str_mv | Gouveia, Paulo D.F. Gouveia, Paulo D.F. http://orcid.org/0000-0003-3049-6230 0000-0003-3049-6230 Torres, Delfim F.M. |
| publishDate | 2006 |
| publisher.none.fl_str_mv | Maplesoft |
| repo_facet_str | urn:repositoryAcronym:ipb{{{_:::_}}}Biblioteca Digital da UPB |
| reponame_str | Biblioteca Digital da UPB |
| repository_id_str | urn:repositoryAcronym:ipb |
| service_str_mv | urn:repositoryAcronym:ipb |
| spelling | engMaplesoftptWe present analytic 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, and which was extended recently to the more general context of optimal control. We show how a Computer Algebra System can be very helpful in finding 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 given.application/octet-streamimage/tiffptAutomatic computation of conservation laws in the calculus of variations and optimal controlPersonalGouveia, Paulo D.F.DSpacehttp://dspace.org/items/41c37437-90c4-4e40-893b-44fe4ae1f159DSpacehttp://dspace.org/items/41c37437-90c4-4e40-893b-44fe4ae1f159GouveiaPaulo D.F.ORCIDhttp://orcid.org0000-0003-3049-6230Scopus Author IDhttps://www.scopus.com20433578000Torres, Delfim F.M.HostingInstitutionOrganizationalBiblioteca Digital da UPBe-mailmailto:dspace@unipb.ptdspace@unipb.pt2010-02-17T17:04:15Z20062006-01-01T00:00:00ZHandlehttp://hdl.handle.net/10198/1970http://purl.org/coar/access_right/c_abf2open accessOptimal controlCalculus of variationsComputer algebraNoether’s theoremSymmetriesConservation laws141543 bytes305200 bytesother research producthttp://purl.org/coar/resource_type/c_8042working paperhttp://purl.org/coar/access_right/c_abf2application/octet-streamfulltexthttps://bibliotecadigital.unipb.pt/bitstreams/3405d3f6-754b-4526-9563-004672bfa6b4/downloadhttp://purl.org/coar/access_right/c_abf2image/tifffulltexthttps://bibliotecadigital.unipb.pt/bitstreams/9634e665-ba8b-4dba-8cf4-cd0ee7858d0a/downloadMaple Application Centre |
| 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 |
| status | SINGLETON |
| subject.fl_str_mv | Optimal control Calculus of variations Computer algebra Noether’s theorem Symmetries Conservation laws |
| title | 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_short | 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 |
| topic | Optimal control Calculus of variations Computer algebra Noether’s theorem Symmetries Conservation laws |
| topic_facet | Optimal control Calculus of variations Computer algebra Noether’s theorem Symmetries Conservation laws |
| url | http://hdl.handle.net/10198/1970 |
| visible | 1 |
Atividades financiadas
Não foram encontrados projetos financiados.