Optimal leader-following consensus of fractional opinion formation models

Detalhes bibliográficos
Autor(a) principal: Almeida, Ricardo
Data de Publicação: 2021
Outros Autores: Kamocki, Rafał, Malinowska, Agnieszka B., Odzijewicz, Tatiana
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/30984
Resumo: This paper deals with a control strategy enforcing consensus in a fractional opinion formation model with leadership, where the interaction rates between followers and the influence rate of the leader are functions of deviations of opinions between agents. The fractional-order derivative determines the impact of the memory during the opinion evolution. The problem of leader-following consensus control is cast in the framework of nonlinear optimal control theory. We study a finite horizon optimal control problem, in which deviations of opinions between agents and with respect to the leader are penalized along with the control that is applied only to the leader. The existence conditions for optimal consensus control are proved and necessary optimality conditions for the considered problem are derived. The results of the paper are illustrated by some examples.
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spelling Optimal leader-following consensus of fractional opinion formation modelsFractional calculusFractional differential systemsOpinion formation modelsConsensusOptimal controlThis paper deals with a control strategy enforcing consensus in a fractional opinion formation model with leadership, where the interaction rates between followers and the influence rate of the leader are functions of deviations of opinions between agents. The fractional-order derivative determines the impact of the memory during the opinion evolution. The problem of leader-following consensus control is cast in the framework of nonlinear optimal control theory. We study a finite horizon optimal control problem, in which deviations of opinions between agents and with respect to the leader are penalized along with the control that is applied only to the leader. The existence conditions for optimal consensus control are proved and necessary optimality conditions for the considered problem are derived. The results of the paper are illustrated by some examples.Elsevier2021-03-23T09:31:46Z2021-01-01T00:00:00Z2021-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/30984eng0377-042710.1016/j.cam.2020.112996Almeida, RicardoKamocki, RafałMalinowska, Agnieszka B.Odzijewicz, Tatianainfo: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:RCAAP2024-02-22T11:59:47Zoai:ria.ua.pt:10773/30984Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:02:57.038112Repositório 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 Optimal leader-following consensus of fractional opinion formation models
title Optimal leader-following consensus of fractional opinion formation models
spellingShingle Optimal leader-following consensus of fractional opinion formation models
Almeida, Ricardo
Fractional calculus
Fractional differential systems
Opinion formation models
Consensus
Optimal control
title_short Optimal leader-following consensus of fractional opinion formation models
title_full Optimal leader-following consensus of fractional opinion formation models
title_fullStr Optimal leader-following consensus of fractional opinion formation models
title_full_unstemmed Optimal leader-following consensus of fractional opinion formation models
title_sort Optimal leader-following consensus of fractional opinion formation models
author Almeida, Ricardo
author_facet Almeida, Ricardo
Kamocki, Rafał
Malinowska, Agnieszka B.
Odzijewicz, Tatiana
author_role author
author2 Kamocki, Rafał
Malinowska, Agnieszka B.
Odzijewicz, Tatiana
author2_role author
author
author
dc.contributor.author.fl_str_mv Almeida, Ricardo
Kamocki, Rafał
Malinowska, Agnieszka B.
Odzijewicz, Tatiana
dc.subject.por.fl_str_mv Fractional calculus
Fractional differential systems
Opinion formation models
Consensus
Optimal control
topic Fractional calculus
Fractional differential systems
Opinion formation models
Consensus
Optimal control
description This paper deals with a control strategy enforcing consensus in a fractional opinion formation model with leadership, where the interaction rates between followers and the influence rate of the leader are functions of deviations of opinions between agents. The fractional-order derivative determines the impact of the memory during the opinion evolution. The problem of leader-following consensus control is cast in the framework of nonlinear optimal control theory. We study a finite horizon optimal control problem, in which deviations of opinions between agents and with respect to the leader are penalized along with the control that is applied only to the leader. The existence conditions for optimal consensus control are proved and necessary optimality conditions for the considered problem are derived. The results of the paper are illustrated by some examples.
publishDate 2021
dc.date.none.fl_str_mv 2021-03-23T09:31:46Z
2021-01-01T00:00:00Z
2021-01-01
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/10773/30984
url http://hdl.handle.net/10773/30984
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0377-0427
10.1016/j.cam.2020.112996
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
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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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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