An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.22/6964 |
Resumo: | The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions. |
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An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance indexFractional optimal control problemLegendre polynomialsOperational matrixLagrange multiplier methodCaputo derivativesRiemann–liouville integralsThe shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.Wiley Online LibraryRepositório Científico do Instituto Politécnico do PortoBhrawy, A. H.Doha, E.H.Machado, J. A. TenreiroEzz-Eldien, S. S.2015-11-20T12:01:55Z20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/6964eng10.1002/asjc.1109info: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:RCAAP2023-03-13T12:47:16Zoai:recipp.ipp.pt:10400.22/6964Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:27:23.492438Repositório 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 |
An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index |
title |
An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index |
spellingShingle |
An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index Bhrawy, A. H. Fractional optimal control problem Legendre polynomials Operational matrix Lagrange multiplier method Caputo derivatives Riemann–liouville integrals |
title_short |
An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index |
title_full |
An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index |
title_fullStr |
An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index |
title_full_unstemmed |
An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index |
title_sort |
An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index |
author |
Bhrawy, A. H. |
author_facet |
Bhrawy, A. H. Doha, E.H. Machado, J. A. Tenreiro Ezz-Eldien, S. S. |
author_role |
author |
author2 |
Doha, E.H. Machado, J. A. Tenreiro Ezz-Eldien, S. S. |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Repositório Científico do Instituto Politécnico do Porto |
dc.contributor.author.fl_str_mv |
Bhrawy, A. H. Doha, E.H. Machado, J. A. Tenreiro Ezz-Eldien, S. S. |
dc.subject.por.fl_str_mv |
Fractional optimal control problem Legendre polynomials Operational matrix Lagrange multiplier method Caputo derivatives Riemann–liouville integrals |
topic |
Fractional optimal control problem Legendre polynomials Operational matrix Lagrange multiplier method Caputo derivatives Riemann–liouville integrals |
description |
The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-11-20T12:01:55Z 2015 2015-01-01T00:00:00Z |
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/10400.22/6964 |
url |
http://hdl.handle.net/10400.22/6964 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1002/asjc.1109 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Wiley Online Library |
publisher.none.fl_str_mv |
Wiley Online Library |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) 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 |
repository.mail.fl_str_mv |
|
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1799131369232662528 |