Second-order analysis and numerical approximation for bang-bang bilinear control problems

We consider bilinear optimal control problems whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient secondorder conditions for bang-bang controls, which guarantee local quadratic growth of the objective functional in L1 . In addi...

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Detalles Bibliográficos
Autores: Casas Rentería, Eduardo|||0000-0002-8364-9416, Wachsmuth, Daniel, Wachsmuth, Gerd
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/15023
Acceso en línea:http://hdl.handle.net/10902/15023
Access Level:acceso abierto
Palabra clave:Bang-bang control
Bilinear controls
Second-order conditions
Sufficient optimality conditions
Error analysis
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spelling Second-order analysis and numerical approximation for bang-bang bilinear control problemsCasas Rentería, Eduardo|||0000-0002-8364-9416Wachsmuth, DanielWachsmuth, GerdBang-bang controlBilinear controlsSecond-order conditionsSufficient optimality conditionsError analysisWe consider bilinear optimal control problems whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient secondorder conditions for bang-bang controls, which guarantee local quadratic growth of the objective functional in L1 . In addition, we prove that for controls that are not bang-bang, no such growth can be expected. Finally, we study the finite-element discretization and prove error estimates of bang-bang controls in L1 -norms.The first author was partially supported by the Spanish Ministerio de Economía Industria y Competitividad under research projects MTM2014-57531-P and MTM2017-83185-P. The second author was partially supported by DFG under grant Wa 3626/1-1.Society for Industrial and Applied MathematicsUniversidad de Cantabria20182018-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttp://hdl.handle.net/10902/15023SIAM Journal on Control and Optimization, 2018, 56(6), 4203-4227reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/150232026-06-02T12:39:31Z
dc.title.none.fl_str_mv Second-order analysis and numerical approximation for bang-bang bilinear control problems
title Second-order analysis and numerical approximation for bang-bang bilinear control problems
spellingShingle Second-order analysis and numerical approximation for bang-bang bilinear control problems
Casas Rentería, Eduardo|||0000-0002-8364-9416
Bang-bang control
Bilinear controls
Second-order conditions
Sufficient optimality conditions
Error analysis
title_short Second-order analysis and numerical approximation for bang-bang bilinear control problems
title_full Second-order analysis and numerical approximation for bang-bang bilinear control problems
title_fullStr Second-order analysis and numerical approximation for bang-bang bilinear control problems
title_full_unstemmed Second-order analysis and numerical approximation for bang-bang bilinear control problems
title_sort Second-order analysis and numerical approximation for bang-bang bilinear control problems
dc.creator.none.fl_str_mv Casas Rentería, Eduardo|||0000-0002-8364-9416
Wachsmuth, Daniel
Wachsmuth, Gerd
author Casas Rentería, Eduardo|||0000-0002-8364-9416
author_facet Casas Rentería, Eduardo|||0000-0002-8364-9416
Wachsmuth, Daniel
Wachsmuth, Gerd
author_role author
author2 Wachsmuth, Daniel
Wachsmuth, Gerd
author2_role author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Bang-bang control
Bilinear controls
Second-order conditions
Sufficient optimality conditions
Error analysis
topic Bang-bang control
Bilinear controls
Second-order conditions
Sufficient optimality conditions
Error analysis
description We consider bilinear optimal control problems whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient secondorder conditions for bang-bang controls, which guarantee local quadratic growth of the objective functional in L1 . In addition, we prove that for controls that are not bang-bang, no such growth can be expected. Finally, we study the finite-element discretization and prove error estimates of bang-bang controls in L1 -norms.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10902/15023
url http://hdl.handle.net/10902/15023
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv SIAM Journal on Control and Optimization, 2018, 56(6), 4203-4227
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869420152672485376
score 15.300724

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