A numerical approach for solving fractional optimal control problems using modified hat functions
Autor(a) principal: | |
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Data de Publicação: | 2019 |
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/10773/26144 |
Resumo: | We introduce a numerical method, based on modified hat functions, for solving a class of fractional optimal control problems. In our scheme, the control and the fractional derivative of the state function are considered as linear combinations of the modified hat functions. The fractional derivative is considered in the Caputo sense while the Riemann-Liouville integral operator is used to give approximations for the state function and some of its derivatives. To this aim, we use the fractional order integration operational matrix of the modified hat functions and some properties of the Caputo derivative and Riemann-Liouville integral operators. Using results of the considered basis functions, solving the fractional optimal control problem is reduced to the solution of a system of nonlinear algebraic equations. An error bound is proved for the approximate optimal value of the performance index obtained by the proposed method. The method is then generalized for solving a class of fractional optimal control problems with inequality constraints. The most important advantages of our method are easy implementation, simple operations, and elimination of numerical integration. Some illustrative examples are considered to demonstrate the effectiveness and accuracy of the proposed technique. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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A numerical approach for solving fractional optimal control problems using modified hat functionsFractional optimal control problemsModified hat functionsOperational matrix of fractional integrationInequality constraintsWe introduce a numerical method, based on modified hat functions, for solving a class of fractional optimal control problems. In our scheme, the control and the fractional derivative of the state function are considered as linear combinations of the modified hat functions. The fractional derivative is considered in the Caputo sense while the Riemann-Liouville integral operator is used to give approximations for the state function and some of its derivatives. To this aim, we use the fractional order integration operational matrix of the modified hat functions and some properties of the Caputo derivative and Riemann-Liouville integral operators. Using results of the considered basis functions, solving the fractional optimal control problem is reduced to the solution of a system of nonlinear algebraic equations. An error bound is proved for the approximate optimal value of the performance index obtained by the proposed method. The method is then generalized for solving a class of fractional optimal control problems with inequality constraints. The most important advantages of our method are easy implementation, simple operations, and elimination of numerical integration. Some illustrative examples are considered to demonstrate the effectiveness and accuracy of the proposed technique.Elsevier2019-112019-11-01T00:00:00Z2020-11-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/26144eng1007-570410.1016/j.cnsns.2019.104849Nemati, SomayehLima, Pedro M.Torres, Delfim F. M.info: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:RCAAP2024-02-22T11:50:36Zoai:ria.ua.pt:10773/26144Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:59:12.315284Repositório 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 |
A numerical approach for solving fractional optimal control problems using modified hat functions |
title |
A numerical approach for solving fractional optimal control problems using modified hat functions |
spellingShingle |
A numerical approach for solving fractional optimal control problems using modified hat functions Nemati, Somayeh Fractional optimal control problems Modified hat functions Operational matrix of fractional integration Inequality constraints |
title_short |
A numerical approach for solving fractional optimal control problems using modified hat functions |
title_full |
A numerical approach for solving fractional optimal control problems using modified hat functions |
title_fullStr |
A numerical approach for solving fractional optimal control problems using modified hat functions |
title_full_unstemmed |
A numerical approach for solving fractional optimal control problems using modified hat functions |
title_sort |
A numerical approach for solving fractional optimal control problems using modified hat functions |
author |
Nemati, Somayeh |
author_facet |
Nemati, Somayeh Lima, Pedro M. Torres, Delfim F. M. |
author_role |
author |
author2 |
Lima, Pedro M. Torres, Delfim F. M. |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Nemati, Somayeh Lima, Pedro M. Torres, Delfim F. M. |
dc.subject.por.fl_str_mv |
Fractional optimal control problems Modified hat functions Operational matrix of fractional integration Inequality constraints |
topic |
Fractional optimal control problems Modified hat functions Operational matrix of fractional integration Inequality constraints |
description |
We introduce a numerical method, based on modified hat functions, for solving a class of fractional optimal control problems. In our scheme, the control and the fractional derivative of the state function are considered as linear combinations of the modified hat functions. The fractional derivative is considered in the Caputo sense while the Riemann-Liouville integral operator is used to give approximations for the state function and some of its derivatives. To this aim, we use the fractional order integration operational matrix of the modified hat functions and some properties of the Caputo derivative and Riemann-Liouville integral operators. Using results of the considered basis functions, solving the fractional optimal control problem is reduced to the solution of a system of nonlinear algebraic equations. An error bound is proved for the approximate optimal value of the performance index obtained by the proposed method. The method is then generalized for solving a class of fractional optimal control problems with inequality constraints. The most important advantages of our method are easy implementation, simple operations, and elimination of numerical integration. Some illustrative examples are considered to demonstrate the effectiveness and accuracy of the proposed technique. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-11 2019-11-01T00:00:00Z 2020-11-01T00:00:00Z |
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/10773/26144 |
url |
http://hdl.handle.net/10773/26144 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1007-5704 10.1016/j.cnsns.2019.104849 |
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 |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
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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1799137646524497920 |