Pontryagin maximum principle for distributed-order fractional systems

Detalhes bibliográficos
Autor(a) principal: Ndaïrou, Faïçal
Data de Publicação: 2021
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/10773/31813
Resumo: We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type. The possibility that admissible controls are subject to pointwise constraints is new and requires more sophisticated techniques to include a maximality condition. We start by proving results on continuity of solutions due to needle-like control perturbations. Then, we derive a differentiability result on the state solutions with respect to the perturbed trajectories. We end by stating and proving the Pontryagin maximum principle for distributed-order fractional optimal control problems, illustrating its applicability with an example.
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spelling Pontryagin maximum principle for distributed-order fractional systemsDistributed-order fractional calculusOptimal controlPontryagin maximum principleNeedle-like variationsWe consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type. The possibility that admissible controls are subject to pointwise constraints is new and requires more sophisticated techniques to include a maximality condition. We start by proving results on continuity of solutions due to needle-like control perturbations. Then, we derive a differentiability result on the state solutions with respect to the perturbed trajectories. We end by stating and proving the Pontryagin maximum principle for distributed-order fractional optimal control problems, illustrating its applicability with an example.MDPI2021-08-11T17:06:47Z2021-08-02T00:00:00Z2021-08-02info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/31813eng10.3390/math9161883Ndaïrou, FaïçalTorres, 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:RCAAP2024-02-22T12:01:21Zoai:ria.ua.pt:10773/31813Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:03:35.786486Repositório 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 Pontryagin maximum principle for distributed-order fractional systems
title Pontryagin maximum principle for distributed-order fractional systems
spellingShingle Pontryagin maximum principle for distributed-order fractional systems
Ndaïrou, Faïçal
Distributed-order fractional calculus
Optimal control
Pontryagin maximum principle
Needle-like variations
title_short Pontryagin maximum principle for distributed-order fractional systems
title_full Pontryagin maximum principle for distributed-order fractional systems
title_fullStr Pontryagin maximum principle for distributed-order fractional systems
title_full_unstemmed Pontryagin maximum principle for distributed-order fractional systems
title_sort Pontryagin maximum principle for distributed-order fractional systems
author Ndaïrou, Faïçal
author_facet Ndaïrou, Faïçal
Torres, Delfim F. M.
author_role author
author2 Torres, Delfim F. M.
author2_role author
dc.contributor.author.fl_str_mv Ndaïrou, Faïçal
Torres, Delfim F. M.
dc.subject.por.fl_str_mv Distributed-order fractional calculus
Optimal control
Pontryagin maximum principle
Needle-like variations
topic Distributed-order fractional calculus
Optimal control
Pontryagin maximum principle
Needle-like variations
description We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type. The possibility that admissible controls are subject to pointwise constraints is new and requires more sophisticated techniques to include a maximality condition. We start by proving results on continuity of solutions due to needle-like control perturbations. Then, we derive a differentiability result on the state solutions with respect to the perturbed trajectories. We end by stating and proving the Pontryagin maximum principle for distributed-order fractional optimal control problems, illustrating its applicability with an example.
publishDate 2021
dc.date.none.fl_str_mv 2021-08-11T17:06:47Z
2021-08-02T00:00:00Z
2021-08-02
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/31813
url http://hdl.handle.net/10773/31813
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.3390/math9161883
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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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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