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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/4805
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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 |
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CONICET Digital (CONICET) |
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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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12.982451 |