Jacobi fields in optimal control: Morse and Maslov indices

Detalhes bibliográficos
Autor(a) principal: Agrachev, Andrei
Data de Publicação: 2022
Outros Autores: Beschastnyi, Ivan
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/36286
Resumo: In this paper we discuss a general framework based on symplectic geometry for the study of second order conditions in constrained variational problems on curves. Using the notion of L-derivatives we construct Jacobi curves, which represent a generalization of Jacobi fields from the classical calculus of variations, but which also works for non-smooth extremals. This construction includes in particular the previously known constructions for specific types of extremals. We state and prove Morse-type theorems that connect the negative inertia index of the Hessian of the problem to some symplectic invariants of Jacobi curves.
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spelling Jacobi fields in optimal control: Morse and Maslov indicesMorse theoremsSpectral flowJacobi fieldsOptimal controlMaslov indexLagrangian GrassmanianIn this paper we discuss a general framework based on symplectic geometry for the study of second order conditions in constrained variational problems on curves. Using the notion of L-derivatives we construct Jacobi curves, which represent a generalization of Jacobi fields from the classical calculus of variations, but which also works for non-smooth extremals. This construction includes in particular the previously known constructions for specific types of extremals. We state and prove Morse-type theorems that connect the negative inertia index of the Hessian of the problem to some symplectic invariants of Jacobi curves.Elsevier2023-02-10T12:19:23Z2022-01-01T00:00:00Z2022-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/36286eng0362-546X10.1016/j.na.2021.112608Agrachev, AndreiBeschastnyi, Ivaninfo: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:RCAAP2024-02-22T12:08:21Zoai:ria.ua.pt:10773/36286Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:06:30.759776Repositório 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 Jacobi fields in optimal control: Morse and Maslov indices
title Jacobi fields in optimal control: Morse and Maslov indices
spellingShingle Jacobi fields in optimal control: Morse and Maslov indices
Agrachev, Andrei
Morse theorems
Spectral flow
Jacobi fields
Optimal control
Maslov index
Lagrangian Grassmanian
title_short Jacobi fields in optimal control: Morse and Maslov indices
title_full Jacobi fields in optimal control: Morse and Maslov indices
title_fullStr Jacobi fields in optimal control: Morse and Maslov indices
title_full_unstemmed Jacobi fields in optimal control: Morse and Maslov indices
title_sort Jacobi fields in optimal control: Morse and Maslov indices
author Agrachev, Andrei
author_facet Agrachev, Andrei
Beschastnyi, Ivan
author_role author
author2 Beschastnyi, Ivan
author2_role author
dc.contributor.author.fl_str_mv Agrachev, Andrei
Beschastnyi, Ivan
dc.subject.por.fl_str_mv Morse theorems
Spectral flow
Jacobi fields
Optimal control
Maslov index
Lagrangian Grassmanian
topic Morse theorems
Spectral flow
Jacobi fields
Optimal control
Maslov index
Lagrangian Grassmanian
description In this paper we discuss a general framework based on symplectic geometry for the study of second order conditions in constrained variational problems on curves. Using the notion of L-derivatives we construct Jacobi curves, which represent a generalization of Jacobi fields from the classical calculus of variations, but which also works for non-smooth extremals. This construction includes in particular the previously known constructions for specific types of extremals. We state and prove Morse-type theorems that connect the negative inertia index of the Hessian of the problem to some symplectic invariants of Jacobi curves.
publishDate 2022
dc.date.none.fl_str_mv 2022-01-01T00:00:00Z
2022-01
2023-02-10T12:19:23Z
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/10773/36286
url http://hdl.handle.net/10773/36286
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0362-546X
10.1016/j.na.2021.112608
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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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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