Discrete time schemes for optimal control problems with monotone controls

Autores
Aragone, Laura Susana; Parente, Lisandro Armando; Philipp, Eduardo Andrés
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this article, we consider the Hamilton–Jacobi–Bellman equation associated with the optimization problem with monotone controls. The problem deals with the infinite horizon case and costs with update coefficients. We study the numerical solution through the discretization in time by finite differences. Without the classical semiconcavity-like assumptions, we prove that the convergence in this problem is of order hγ in contrast with the order hγ/2 valid for general control problems. This difference arises from the simple and precise way the monotone controls can be approximated. We illustrate the result with a simple example.
Fil: Aragone, Laura Susana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y Sistemas; Argentina
Fil: Parente, Lisandro Armando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y Sistemas; Argentina
Fil: Philipp, Eduardo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y Sistemas; Argentina
Materia
MONOTONE OPTIMAL CONTROL PROBLEMS
HJB EQUATIONS
NUMERICAL SOLUTIONS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/4805

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network_name_str CONICET Digital (CONICET)
spelling Discrete time schemes for optimal control problems with monotone controlsAragone, Laura SusanaParente, Lisandro ArmandoPhilipp, Eduardo AndrésMONOTONE OPTIMAL CONTROL PROBLEMSHJB EQUATIONSNUMERICAL SOLUTIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this article, we consider the Hamilton–Jacobi–Bellman equation associated with the optimization problem with monotone controls. The problem deals with the infinite horizon case and costs with update coefficients. We study the numerical solution through the discretization in time by finite differences. Without the classical semiconcavity-like assumptions, we prove that the convergence in this problem is of order hγ in contrast with the order hγ/2 valid for general control problems. This difference arises from the simple and precise way the monotone controls can be approximated. We illustrate the result with a simple example.Fil: Aragone, Laura Susana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y Sistemas; ArgentinaFil: Parente, Lisandro Armando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y Sistemas; ArgentinaFil: Philipp, Eduardo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y Sistemas; ArgentinaSpringer2015-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/4805Aragone, Laura Susana; Parente, Lisandro Armando; Philipp, Eduardo Andrés; Discrete time schemes for optimal control problems with monotone controls; Springer; Computational And Applied Mathematics; 34; 3; 10-2015; 847-8630101-8205enginfo:eu-repo/semantics/altIdentifier/issn/0101-8205info:eu-repo/semantics/altIdentifier/doi/10.1007/s40314-014-0149-4info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s40314-014-0149-4info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs40314-014-0149-4info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:07:11Zoai:ri.conicet.gov.ar:11336/4805instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:07:11.331CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Discrete time schemes for optimal control problems with monotone controls
title Discrete time schemes for optimal control problems with monotone controls
spellingShingle Discrete time schemes for optimal control problems with monotone controls
Aragone, Laura Susana
MONOTONE OPTIMAL CONTROL PROBLEMS
HJB EQUATIONS
NUMERICAL SOLUTIONS
title_short Discrete time schemes for optimal control problems with monotone controls
title_full Discrete time schemes for optimal control problems with monotone controls
title_fullStr Discrete time schemes for optimal control problems with monotone controls
title_full_unstemmed Discrete time schemes for optimal control problems with monotone controls
title_sort Discrete time schemes for optimal control problems with monotone controls
dc.creator.none.fl_str_mv Aragone, Laura Susana
Parente, Lisandro Armando
Philipp, Eduardo Andrés
author Aragone, Laura Susana
author_facet Aragone, Laura Susana
Parente, Lisandro Armando
Philipp, Eduardo Andrés
author_role author
author2 Parente, Lisandro Armando
Philipp, Eduardo Andrés
author2_role author
author
dc.subject.none.fl_str_mv MONOTONE OPTIMAL CONTROL PROBLEMS
HJB EQUATIONS
NUMERICAL SOLUTIONS
topic MONOTONE OPTIMAL CONTROL PROBLEMS
HJB EQUATIONS
NUMERICAL SOLUTIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this article, we consider the Hamilton–Jacobi–Bellman equation associated with the optimization problem with monotone controls. The problem deals with the infinite horizon case and costs with update coefficients. We study the numerical solution through the discretization in time by finite differences. Without the classical semiconcavity-like assumptions, we prove that the convergence in this problem is of order hγ in contrast with the order hγ/2 valid for general control problems. This difference arises from the simple and precise way the monotone controls can be approximated. We illustrate the result with a simple example.
Fil: Aragone, Laura Susana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y Sistemas; Argentina
Fil: Parente, Lisandro Armando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y Sistemas; Argentina
Fil: Philipp, Eduardo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y Sistemas; Argentina
description In this article, we consider the Hamilton–Jacobi–Bellman equation associated with the optimization problem with monotone controls. The problem deals with the infinite horizon case and costs with update coefficients. We study the numerical solution through the discretization in time by finite differences. Without the classical semiconcavity-like assumptions, we prove that the convergence in this problem is of order hγ in contrast with the order hγ/2 valid for general control problems. This difference arises from the simple and precise way the monotone controls can be approximated. We illustrate the result with a simple example.
publishDate 2015
dc.date.none.fl_str_mv 2015-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/4805
Aragone, Laura Susana; Parente, Lisandro Armando; Philipp, Eduardo Andrés; Discrete time schemes for optimal control problems with monotone controls; Springer; Computational And Applied Mathematics; 34; 3; 10-2015; 847-863
0101-8205
url http://hdl.handle.net/11336/4805
identifier_str_mv Aragone, Laura Susana; Parente, Lisandro Armando; Philipp, Eduardo Andrés; Discrete time schemes for optimal control problems with monotone controls; Springer; Computational And Applied Mathematics; 34; 3; 10-2015; 847-863
0101-8205
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0101-8205
info:eu-repo/semantics/altIdentifier/doi/10.1007/s40314-014-0149-4
info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s40314-014-0149-4
info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs40314-014-0149-4
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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