Second order analysis for bang-bang control problems of PDEs

In this paper, we derive some sufficient second order optimality conditions for control problems of partial differential equations (PDEs) when the cost functional does not involve the usual quadratic term for the control or higher nonlinearities for it. Though not always, in this situation the optimal...

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Detalles Bibliográficos
Autor: Casas Rentería, Eduardo|||0000-0002-8364-9416
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/2199
Acceso en línea:http://hdl.handle.net/10902/2199
Access Level:acceso abierto
Palabra clave:Optimal control
Semilinear partial differential equation
Second order optimality conditions
Bang-bang controls
Sparse controls
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spelling Second order analysis for bang-bang control problems of PDEsCasas Rentería, Eduardo|||0000-0002-8364-9416Optimal controlSemilinear partial differential equationSecond order optimality conditionsBang-bang controlsSparse controlsIn this paper, we derive some sufficient second order optimality conditions for control problems of partial differential equations (PDEs) when the cost functional does not involve the usual quadratic term for the control or higher nonlinearities for it. Though not always, in this situation the optimal control is typically bang-bang. Two different control problems are studied. The second differs from the first in the presence of the L1 norm of the control. This term leads to optimal controls that are sparse and usually take only three different values (we call them bang-bang-bang controls). Though the proofs are detailed in the case of a semilinear elliptic state equation, the approach can be extended to parabolic control problems. Some hints are provided in the last section to extend the results.This work was supported by the Spanish Ministerio de Economía y Competitividad under project MTM2011-22711Society for Industrial and Applied MathematicsUniversidad de Cantabria20122012-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttp://hdl.handle.net/10902/2199SIAM Journal on Control and Optimization, 2012, 50(4), 2355–2372reponame: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:10902/21992026-06-02T12:39:31Z
dc.title.none.fl_str_mv Second order analysis for bang-bang control problems of PDEs
title Second order analysis for bang-bang control problems of PDEs
spellingShingle Second order analysis for bang-bang control problems of PDEs
Casas Rentería, Eduardo|||0000-0002-8364-9416
Optimal control
Semilinear partial differential equation
Second order optimality conditions
Bang-bang controls
Sparse controls
title_short Second order analysis for bang-bang control problems of PDEs
title_full Second order analysis for bang-bang control problems of PDEs
title_fullStr Second order analysis for bang-bang control problems of PDEs
title_full_unstemmed Second order analysis for bang-bang control problems of PDEs
title_sort Second order analysis for bang-bang control problems of PDEs
dc.creator.none.fl_str_mv Casas Rentería, Eduardo|||0000-0002-8364-9416
author Casas Rentería, Eduardo|||0000-0002-8364-9416
author_facet Casas Rentería, Eduardo|||0000-0002-8364-9416
author_role author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Optimal control
Semilinear partial differential equation
Second order optimality conditions
Bang-bang controls
Sparse controls
topic Optimal control
Semilinear partial differential equation
Second order optimality conditions
Bang-bang controls
Sparse controls
description In this paper, we derive some sufficient second order optimality conditions for control problems of partial differential equations (PDEs) when the cost functional does not involve the usual quadratic term for the control or higher nonlinearities for it. Though not always, in this situation the optimal control is typically bang-bang. Two different control problems are studied. The second differs from the first in the presence of the L1 norm of the control. This term leads to optimal controls that are sparse and usually take only three different values (we call them bang-bang-bang controls). Though the proofs are detailed in the case of a semilinear elliptic state equation, the approach can be extended to parabolic control problems. Some hints are provided in the last section to extend the results.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-01-01
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/10902/2199
url http://hdl.handle.net/10902/2199
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, 2012, 50(4), 2355–2372
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
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score 15,30478

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