Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems

Detalhes bibliográficos
Autor(a) principal: Ndaïrou, Faïçal
Data de Publicação: 2023
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/10773/39835
Resumo: We introduce a new optimal control problem where the controlled dynamical system depends on multi-order (incommensurate) fractional differential equations. The cost functional to be maximized is of Bolza type and depends on incommensurate Caputo fractional-orders derivatives. We establish continuity and differentiability of the state solutions with respect to perturbed trajectories. Then, we state and prove a Pontryagin maximum principle for incommensurate Caputo fractional optimal control problems. Finally, we give an example, illustrating the applicability of our Pontryagin maximum principle.
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spelling Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control ProblemsIncommensurate fractional-orders derivativesFractional optimal controlContinuity and differentiability of state trajectoriesNeedle-like variationsWe introduce a new optimal control problem where the controlled dynamical system depends on multi-order (incommensurate) fractional differential equations. The cost functional to be maximized is of Bolza type and depends on incommensurate Caputo fractional-orders derivatives. We establish continuity and differentiability of the state solutions with respect to perturbed trajectories. Then, we state and prove a Pontryagin maximum principle for incommensurate Caputo fractional optimal control problems. Finally, we give an example, illustrating the applicability of our Pontryagin maximum principle.MDPI2023-12-15T16:38:26Z2023-10-09T00:00:00Z2023-10-09info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/39835eng2227-739010.3390/math11194218Ndaïrou, 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:RCAAP2024-02-22T12:17:22Zoai:ria.ua.pt:10773/39835Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:09:44.970381Repositório 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 Incommensurate Fractional-Orders Optimal Control Problems
title Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems
spellingShingle Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems
Ndaïrou, Faïçal
Incommensurate fractional-orders derivatives
Fractional optimal control
Continuity and differentiability of state trajectories
Needle-like variations
title_short Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems
title_full Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems
title_fullStr Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems
title_full_unstemmed Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems
title_sort Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems
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 Incommensurate fractional-orders derivatives
Fractional optimal control
Continuity and differentiability of state trajectories
Needle-like variations
topic Incommensurate fractional-orders derivatives
Fractional optimal control
Continuity and differentiability of state trajectories
Needle-like variations
description We introduce a new optimal control problem where the controlled dynamical system depends on multi-order (incommensurate) fractional differential equations. The cost functional to be maximized is of Bolza type and depends on incommensurate Caputo fractional-orders derivatives. We establish continuity and differentiability of the state solutions with respect to perturbed trajectories. Then, we state and prove a Pontryagin maximum principle for incommensurate Caputo fractional optimal control problems. Finally, we give an example, illustrating the applicability of our Pontryagin maximum principle.
publishDate 2023
dc.date.none.fl_str_mv 2023-12-15T16:38:26Z
2023-10-09T00:00:00Z
2023-10-09
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/10773/39835
url http://hdl.handle.net/10773/39835
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2227-7390
10.3390/math11194218
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 MDPI
publisher.none.fl_str_mv MDPI
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
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