Regional controllability and minimum energy control of delayed caputo fractional-order linear systems

Detalhes bibliográficos
Autor(a) principal: Karite, Touria
Data de Publicação: 2022
Outros Autores: Khazari, Adil, 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/10773/35547
Resumo: We study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under consideration. Afterward, we formulate the notion of regional controllability for fractional systems with control delays and give some of their important properties. Our main method consists of defining an attainable set, which allows us to prove exact and weak controllability. Moreover, the main results include not only those of controllability but also a powerful Hilbert uniqueness method, which allows us to solve the minimum energy optimal control problem. More precisely, an explicit control is obtained that drives the system from an initial given state to a desired regional state with minimum energy. Two examples are given to illustrate the obtained theoretical results.
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spelling Regional controllability and minimum energy control of delayed caputo fractional-order linear systemsRegional controllabilityFractional-order systemsCaputo derivativesControl delaysOptimal controlMinimum energyWe study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under consideration. Afterward, we formulate the notion of regional controllability for fractional systems with control delays and give some of their important properties. Our main method consists of defining an attainable set, which allows us to prove exact and weak controllability. Moreover, the main results include not only those of controllability but also a powerful Hilbert uniqueness method, which allows us to solve the minimum energy optimal control problem. More precisely, an explicit control is obtained that drives the system from an initial given state to a desired regional state with minimum energy. Two examples are given to illustrate the obtained theoretical results.MDPI2022-12-22T16:47:57Z2022-12-18T00:00:00Z2022-12-18info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/35547eng2227-739010.3390/math10244813Karite, TouriaKhazari, AdilTorres, 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:RCAAP2024-02-22T12:08:18Zoai:ria.ua.pt:10773/35547Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:06:29.229526Repositório 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 Regional controllability and minimum energy control of delayed caputo fractional-order linear systems
title Regional controllability and minimum energy control of delayed caputo fractional-order linear systems
spellingShingle Regional controllability and minimum energy control of delayed caputo fractional-order linear systems
Karite, Touria
Regional controllability
Fractional-order systems
Caputo derivatives
Control delays
Optimal control
Minimum energy
title_short Regional controllability and minimum energy control of delayed caputo fractional-order linear systems
title_full Regional controllability and minimum energy control of delayed caputo fractional-order linear systems
title_fullStr Regional controllability and minimum energy control of delayed caputo fractional-order linear systems
title_full_unstemmed Regional controllability and minimum energy control of delayed caputo fractional-order linear systems
title_sort Regional controllability and minimum energy control of delayed caputo fractional-order linear systems
author Karite, Touria
author_facet Karite, Touria
Khazari, Adil
Torres, Delfim F. M.
author_role author
author2 Khazari, Adil
Torres, Delfim F. M.
author2_role author
author
dc.contributor.author.fl_str_mv Karite, Touria
Khazari, Adil
Torres, Delfim F. M.
dc.subject.por.fl_str_mv Regional controllability
Fractional-order systems
Caputo derivatives
Control delays
Optimal control
Minimum energy
topic Regional controllability
Fractional-order systems
Caputo derivatives
Control delays
Optimal control
Minimum energy
description We study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under consideration. Afterward, we formulate the notion of regional controllability for fractional systems with control delays and give some of their important properties. Our main method consists of defining an attainable set, which allows us to prove exact and weak controllability. Moreover, the main results include not only those of controllability but also a powerful Hilbert uniqueness method, which allows us to solve the minimum energy optimal control problem. More precisely, an explicit control is obtained that drives the system from an initial given state to a desired regional state with minimum energy. Two examples are given to illustrate the obtained theoretical results.
publishDate 2022
dc.date.none.fl_str_mv 2022-12-22T16:47:57Z
2022-12-18T00:00:00Z
2022-12-18
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/10773/35547
url http://hdl.handle.net/10773/35547
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2227-7390
10.3390/math10244813
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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