On the shooting algorithm for partially affine control problems
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Repositório Institucional do FGV (FGV Repositório Digital) |
Texto Completo: | https://hdl.handle.net/10438/29674 |
Resumo: | In this thesis we propose a shooting algorithm for partially affine optimal control problems, this is, systems in which the controls appear both linearly and nonlinearly in the dynamics. Since the shooting system generally has more equations than unknowns, the algorithm relies on the Gauss-Newton method. As a consequence, the convergence is locally quadratic provided that the derivative of the shooting function is Lipschitz continuous at the optimal solution. We provide a proof of the convergence for the proposed algorithm using recently developed second order conditions for weak optimality of partially affine problems. We illustrate the applicability of the algorithm by solving an optimal treatment-vaccination epidemiological problem. |
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Machado, João MiguelEscolas::EMApBonnans, Joseph FrédéricGuglielmi, RobertoSoledad Aronna, Maria2020-09-17T10:36:18Z2020-09-17T10:36:18Z2020-08-12https://hdl.handle.net/10438/29674In this thesis we propose a shooting algorithm for partially affine optimal control problems, this is, systems in which the controls appear both linearly and nonlinearly in the dynamics. Since the shooting system generally has more equations than unknowns, the algorithm relies on the Gauss-Newton method. As a consequence, the convergence is locally quadratic provided that the derivative of the shooting function is Lipschitz continuous at the optimal solution. We provide a proof of the convergence for the proposed algorithm using recently developed second order conditions for weak optimality of partially affine problems. We illustrate the applicability of the algorithm by solving an optimal treatment-vaccination epidemiological problem.engShooting algorithmOptimal control problemsMatemáticaTeoria do controleAlgoritmosCálculo das variaçõesModelos matemáticosOn the shooting algorithm for partially affine control problemsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis2020-08-12reponame:Repositório Institucional do FGV (FGV Repositório Digital)instname:Fundação Getulio Vargas (FGV)instacron:FGVinfo:eu-repo/semantics/openAccessTEXTmain.pdf.txtmain.pdf.txtExtracted texttext/plain103439https://repositorio.fgv.br/bitstreams/bab69ca8-8a3e-422f-b602-8ec35caebad8/download45667458b6802931d301173905116873MD55THUMBNAILmain.pdf.jpgmain.pdf.jpgGenerated 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dc.title.eng.fl_str_mv |
On the shooting algorithm for partially affine control problems |
title |
On the shooting algorithm for partially affine control problems |
spellingShingle |
On the shooting algorithm for partially affine control problems Machado, João Miguel Shooting algorithm Optimal control problems Matemática Teoria do controle Algoritmos Cálculo das variações Modelos matemáticos |
title_short |
On the shooting algorithm for partially affine control problems |
title_full |
On the shooting algorithm for partially affine control problems |
title_fullStr |
On the shooting algorithm for partially affine control problems |
title_full_unstemmed |
On the shooting algorithm for partially affine control problems |
title_sort |
On the shooting algorithm for partially affine control problems |
author |
Machado, João Miguel |
author_facet |
Machado, João Miguel |
author_role |
author |
dc.contributor.unidadefgv.por.fl_str_mv |
Escolas::EMAp |
dc.contributor.member.none.fl_str_mv |
Bonnans, Joseph Frédéric Guglielmi, Roberto |
dc.contributor.author.fl_str_mv |
Machado, João Miguel |
dc.contributor.advisor1.fl_str_mv |
Soledad Aronna, Maria |
contributor_str_mv |
Soledad Aronna, Maria |
dc.subject.eng.fl_str_mv |
Shooting algorithm Optimal control problems |
topic |
Shooting algorithm Optimal control problems Matemática Teoria do controle Algoritmos Cálculo das variações Modelos matemáticos |
dc.subject.area.por.fl_str_mv |
Matemática |
dc.subject.bibliodata.por.fl_str_mv |
Teoria do controle Algoritmos Cálculo das variações Modelos matemáticos |
description |
In this thesis we propose a shooting algorithm for partially affine optimal control problems, this is, systems in which the controls appear both linearly and nonlinearly in the dynamics. Since the shooting system generally has more equations than unknowns, the algorithm relies on the Gauss-Newton method. As a consequence, the convergence is locally quadratic provided that the derivative of the shooting function is Lipschitz continuous at the optimal solution. We provide a proof of the convergence for the proposed algorithm using recently developed second order conditions for weak optimality of partially affine problems. We illustrate the applicability of the algorithm by solving an optimal treatment-vaccination epidemiological problem. |
publishDate |
2020 |
dc.date.accessioned.fl_str_mv |
2020-09-17T10:36:18Z |
dc.date.available.fl_str_mv |
2020-09-17T10:36:18Z |
dc.date.issued.fl_str_mv |
2020-08-12 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://hdl.handle.net/10438/29674 |
url |
https://hdl.handle.net/10438/29674 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional do FGV (FGV Repositório Digital) instname:Fundação Getulio Vargas (FGV) instacron:FGV |
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