Multi-objective control problems for parabolic and dispersive systems
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/45917 |
Resumo: | This thesis is dedicated to the study of some multi-objective control problems for partial di erential equations. Usually, problems containing many objectives are not well-posed, since one objective may completely determine the control, turning the others objectives impossible to reach. For this reason, concepts of equilibrium (or efficiency) are normally applied to nd controls which are acceptable, in the sense they make the best decision possible according to some prescribed goals. By applying the so called Stackelberg-Nash strategy, we consider a hierarchy, in the sense that we have one control which we call the leader, and other controls which we call the followers. Once the leader policy is fixed, the followers intend to be in equilibrium according to their targets, this is what we call Stackelberg's Method. Once this hierarchy is established, we determine the followers in such a way they accomplish their objectives in a optimal way, and to do that a concept of equilibrium is applied. In this work, we apply the concept of Nash Equilibrium, which correspond to a non-cooperative strategy. By combining the Stackelberg's Method and the concept of Nash Equilibrium is what we call Stackelberg-Nash strategy. This thesis is divided into two chapters. In each of them, we solve a multi-objective control problems by following the Stackelberg-Nash strategy. In the rst chapter, we consider a linear system of parabolic equations and prove that the Stackelberg-Nash strategy can be applied under some suitable conditions for the coupling coe cients. In the second one, we consider the nonlinear Korteweg-de Vries (KdV) equation, which has a very di erent nature of parabolic equations, and the same method is applied. |
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LIMA, Islanita Cecília Alcântara de Albuquerquehttp://lattes.cnpq.br/6358368837129919http://lattes.cnpq.br/2628861259158973SANTOS, Maurício Cardoso2022-08-24T14:26:37Z2022-08-24T14:26:37Z2020-02-28LIMA, Islanita Cecília Alcântara de Albuquerque. Multi-objective control problems for parabolic and dispersive systems. 2020. Tese (Doutorado em Matemática) – Universidade Federal de Pernambuco, Recife, 2020.https://repositorio.ufpe.br/handle/123456789/45917This thesis is dedicated to the study of some multi-objective control problems for partial di erential equations. Usually, problems containing many objectives are not well-posed, since one objective may completely determine the control, turning the others objectives impossible to reach. For this reason, concepts of equilibrium (or efficiency) are normally applied to nd controls which are acceptable, in the sense they make the best decision possible according to some prescribed goals. By applying the so called Stackelberg-Nash strategy, we consider a hierarchy, in the sense that we have one control which we call the leader, and other controls which we call the followers. Once the leader policy is fixed, the followers intend to be in equilibrium according to their targets, this is what we call Stackelberg's Method. Once this hierarchy is established, we determine the followers in such a way they accomplish their objectives in a optimal way, and to do that a concept of equilibrium is applied. In this work, we apply the concept of Nash Equilibrium, which correspond to a non-cooperative strategy. By combining the Stackelberg's Method and the concept of Nash Equilibrium is what we call Stackelberg-Nash strategy. This thesis is divided into two chapters. In each of them, we solve a multi-objective control problems by following the Stackelberg-Nash strategy. In the rst chapter, we consider a linear system of parabolic equations and prove that the Stackelberg-Nash strategy can be applied under some suitable conditions for the coupling coe cients. In the second one, we consider the nonlinear Korteweg-de Vries (KdV) equation, which has a very di erent nature of parabolic equations, and the same method is applied.Esta tese é dedicada ao estudo de alguns problemas de controle multiobjetivos para equações diferenciais parciais. Normalmente, problemas desta natureza não são bem colocados, uma vez que um objetivo pode determinar completamente o controle, tornando impossível o alcance dos demais. Por esta razão, conceitos de equilíbrio (ou eficiência) são normalmente aplicados para encontrar controles que são aceitáveis, no sentido em que tomam a melhor decisão possível de acordo com alguns objetivos prescritos. Ao aplicar a chamada estratégia de Stackelberg-Nash, nós consideramos uma hierarquia, no sentido de que temos um controle que chamamos de líder e outros controles que chamamos de seguidores. Um vez que a escolha do líder é fixada, os seguidores pretendem estar em equilíbrio de acordo com seus objetivos, isto é o que chamamos de Método de Stackelberg. Uma vez que essa hierarquia é estabelecida, nós determinamos os seguidores de modo que eles cumpram seus objetivos de maneira ideal, e para isso um conceito de equilíbrio é aplicado. Neste trabalho, nós aplicamos o conceito de Equilíbrio de Nash, que corresponde a uma estratégia não-cooperativa. Combinando o método de Stackelberg e o conceito do equilíbrio de Nash, temos o que chamamos de estratégia de Stackelberg-Nash. Esta tese é dividida em dois capítulos. Em cada um deles, nós resolvemos um problema de controle multiobjetivo seguindo a estratégia Stackelberg-Nash. No primerio capítulo, nós consideramos um sistema linear de equações parabólicas e provamos que a estratégia Stackelberg-Nash pode ser aplicada sob algumas condições adequadas para os coe cientes de acoplamento. No segundo capítulo, nós consideramos a equação de Korteweg-de Vries (KdV) não linear, que tem uma natureza muito diferente de equações parabólicas, e o mesmo método é aplicado.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em MatematicaUFPEBrasilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/embargoedAccessAnáliseSistemas parabólicosMulti-objective control problems for parabolic and dispersive systemsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPEORIGINALTESE Islanita Cecília Alcantara de Albuquerque Lima.pdfTESE Islanita Cecília Alcantara de Albuquerque Lima.pdfapplication/pdf721179https://repositorio.ufpe.br/bitstream/123456789/45917/1/TESE%20Islanita%20Cec%c3%adlia%20Alcantara%20de%20Albuquerque%20Lima.pdf3213a82d2f8f5abfd34a3e874258bf07MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufpe.br/bitstream/123456789/45917/2/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD52LICENSElicense.txtlicense.txttext/plain; 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dc.title.pt_BR.fl_str_mv |
Multi-objective control problems for parabolic and dispersive systems |
title |
Multi-objective control problems for parabolic and dispersive systems |
spellingShingle |
Multi-objective control problems for parabolic and dispersive systems LIMA, Islanita Cecília Alcântara de Albuquerque Análise Sistemas parabólicos |
title_short |
Multi-objective control problems for parabolic and dispersive systems |
title_full |
Multi-objective control problems for parabolic and dispersive systems |
title_fullStr |
Multi-objective control problems for parabolic and dispersive systems |
title_full_unstemmed |
Multi-objective control problems for parabolic and dispersive systems |
title_sort |
Multi-objective control problems for parabolic and dispersive systems |
author |
LIMA, Islanita Cecília Alcântara de Albuquerque |
author_facet |
LIMA, Islanita Cecília Alcântara de Albuquerque |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/6358368837129919 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/2628861259158973 |
dc.contributor.author.fl_str_mv |
LIMA, Islanita Cecília Alcântara de Albuquerque |
dc.contributor.advisor1.fl_str_mv |
SANTOS, Maurício Cardoso |
contributor_str_mv |
SANTOS, Maurício Cardoso |
dc.subject.por.fl_str_mv |
Análise Sistemas parabólicos |
topic |
Análise Sistemas parabólicos |
description |
This thesis is dedicated to the study of some multi-objective control problems for partial di erential equations. Usually, problems containing many objectives are not well-posed, since one objective may completely determine the control, turning the others objectives impossible to reach. For this reason, concepts of equilibrium (or efficiency) are normally applied to nd controls which are acceptable, in the sense they make the best decision possible according to some prescribed goals. By applying the so called Stackelberg-Nash strategy, we consider a hierarchy, in the sense that we have one control which we call the leader, and other controls which we call the followers. Once the leader policy is fixed, the followers intend to be in equilibrium according to their targets, this is what we call Stackelberg's Method. Once this hierarchy is established, we determine the followers in such a way they accomplish their objectives in a optimal way, and to do that a concept of equilibrium is applied. In this work, we apply the concept of Nash Equilibrium, which correspond to a non-cooperative strategy. By combining the Stackelberg's Method and the concept of Nash Equilibrium is what we call Stackelberg-Nash strategy. This thesis is divided into two chapters. In each of them, we solve a multi-objective control problems by following the Stackelberg-Nash strategy. In the rst chapter, we consider a linear system of parabolic equations and prove that the Stackelberg-Nash strategy can be applied under some suitable conditions for the coupling coe cients. In the second one, we consider the nonlinear Korteweg-de Vries (KdV) equation, which has a very di erent nature of parabolic equations, and the same method is applied. |
publishDate |
2020 |
dc.date.issued.fl_str_mv |
2020-02-28 |
dc.date.accessioned.fl_str_mv |
2022-08-24T14:26:37Z |
dc.date.available.fl_str_mv |
2022-08-24T14:26:37Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
LIMA, Islanita Cecília Alcântara de Albuquerque. Multi-objective control problems for parabolic and dispersive systems. 2020. Tese (Doutorado em Matemática) – Universidade Federal de Pernambuco, Recife, 2020. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufpe.br/handle/123456789/45917 |
identifier_str_mv |
LIMA, Islanita Cecília Alcântara de Albuquerque. Multi-objective control problems for parabolic and dispersive systems. 2020. Tese (Doutorado em Matemática) – Universidade Federal de Pernambuco, Recife, 2020. |
url |
https://repositorio.ufpe.br/handle/123456789/45917 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
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http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
embargoedAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
dc.publisher.program.fl_str_mv |
Programa de Pos Graduacao em Matematica |
dc.publisher.initials.fl_str_mv |
UFPE |
dc.publisher.country.fl_str_mv |
Brasil |
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Universidade Federal de Pernambuco |
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Repositório Institucional da UFPE |
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