Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems
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/10773/24646 |
Resumo: | This paper presents three direct methods based on Grünwald–Letnikov, trapezoidal and Simpson fractional integral formulas to solve fractional optimal control problems (FOCPs). At first, the fractional integral form of FOCP is considered, then the fractional integral is approximated by Grünwald–Letnikov, trapezoidal and Simpson formulas in a matrix approach. Thereafter, the performance index is approximated either by trapezoidal or Simpson quadrature. As a result, FOCPs are reduced to nonlinear programming problems, which can be solved by many well-developed algorithms. To improve the efficiency of the presented method, the gradient of the objective function and the Jacobian of constraints are prepared in closed forms. It is pointed out that the implementation of the methods is simple and, due to the fact that there is no need to derive necessary conditions, the methods can be simply and quickly used to solve a wide class of FOCPs. The efficiency and reliability of the presented methods are assessed by ample numerical tests involving a free final time with path constraint FOCP, a bang-bang FOCP and an optimal control of a fractional-order HIV-immune system. |
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Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problemsFractional optimal controlDirect numerical solutionFractional integration matrixGrünwald–LetnikovTrapezoidal and Simpson fractional integral formulasThis paper presents three direct methods based on Grünwald–Letnikov, trapezoidal and Simpson fractional integral formulas to solve fractional optimal control problems (FOCPs). At first, the fractional integral form of FOCP is considered, then the fractional integral is approximated by Grünwald–Letnikov, trapezoidal and Simpson formulas in a matrix approach. Thereafter, the performance index is approximated either by trapezoidal or Simpson quadrature. As a result, FOCPs are reduced to nonlinear programming problems, which can be solved by many well-developed algorithms. To improve the efficiency of the presented method, the gradient of the objective function and the Jacobian of constraints are prepared in closed forms. It is pointed out that the implementation of the methods is simple and, due to the fact that there is no need to derive necessary conditions, the methods can be simply and quickly used to solve a wide class of FOCPs. The efficiency and reliability of the presented methods are assessed by ample numerical tests involving a free final time with path constraint FOCP, a bang-bang FOCP and an optimal control of a fractional-order HIV-immune system.Elsevier2020-02-01T00:00:00Z2019-02-01T00:00:00Z2019-02info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/24646eng1007-570410.1016/j.cnsns.2018.05.011Salati, Abubakar BelloShamsi, MostafaTorres, Delfim F. M.info:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:47:50Zoai:ria.ua.pt:10773/24646Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:58:03.542815Repositório 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 |
Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems |
title |
Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems |
spellingShingle |
Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems Salati, Abubakar Bello Fractional optimal control Direct numerical solution Fractional integration matrix Grünwald–Letnikov Trapezoidal and Simpson fractional integral formulas |
title_short |
Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems |
title_full |
Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems |
title_fullStr |
Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems |
title_full_unstemmed |
Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems |
title_sort |
Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems |
author |
Salati, Abubakar Bello |
author_facet |
Salati, Abubakar Bello Shamsi, Mostafa Torres, Delfim F. M. |
author_role |
author |
author2 |
Shamsi, Mostafa Torres, Delfim F. M. |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Salati, Abubakar Bello Shamsi, Mostafa Torres, Delfim F. M. |
dc.subject.por.fl_str_mv |
Fractional optimal control Direct numerical solution Fractional integration matrix Grünwald–Letnikov Trapezoidal and Simpson fractional integral formulas |
topic |
Fractional optimal control Direct numerical solution Fractional integration matrix Grünwald–Letnikov Trapezoidal and Simpson fractional integral formulas |
description |
This paper presents three direct methods based on Grünwald–Letnikov, trapezoidal and Simpson fractional integral formulas to solve fractional optimal control problems (FOCPs). At first, the fractional integral form of FOCP is considered, then the fractional integral is approximated by Grünwald–Letnikov, trapezoidal and Simpson formulas in a matrix approach. Thereafter, the performance index is approximated either by trapezoidal or Simpson quadrature. As a result, FOCPs are reduced to nonlinear programming problems, which can be solved by many well-developed algorithms. To improve the efficiency of the presented method, the gradient of the objective function and the Jacobian of constraints are prepared in closed forms. It is pointed out that the implementation of the methods is simple and, due to the fact that there is no need to derive necessary conditions, the methods can be simply and quickly used to solve a wide class of FOCPs. The efficiency and reliability of the presented methods are assessed by ample numerical tests involving a free final time with path constraint FOCP, a bang-bang FOCP and an optimal control of a fractional-order HIV-immune system. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-02-01T00:00:00Z 2019-02 2020-02-01T00:00:00Z |
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/10773/24646 |
url |
http://hdl.handle.net/10773/24646 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1007-5704 10.1016/j.cnsns.2018.05.011 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/embargoedAccess |
eu_rights_str_mv |
embargoedAccess |
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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1799137634797223936 |