Optimal Bounds for POD Approximations of Infinite Horizon Control Problems Based on Time Derivatives

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Comm...

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Autores: De Frutos, Javier, García-Archilla, Bosco, Novo, Julia
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/172155
Acceso en línea:https://hdl.handle.net/11441/172155
https://doi.org/10.1007/s10915-025-02833-0
Access Level:acceso abierto
Palabra clave:Dynamic programming
Hamilton–Jacobi–Bellman equation
Optimal control
Proper orthogonal decomposition
Snapshots based on time derivatives
Error analysis
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spelling Optimal Bounds for POD Approximations of Infinite Horizon Control Problems Based on Time DerivativesDe Frutos, JavierGarcía-Archilla, BoscoNovo, JuliaDynamic programmingHamilton–Jacobi–Bellman equationOptimal controlProper orthogonal decompositionSnapshots based on time derivativesError analysisThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.In this paper we consider the numerical approximation of infinite horizon problems via the dynamic programming approach. The value function of the problem solves a Hamilton–Jacobi–Bellman equation that is approximated by a fully discrete method. It is known that the numerical problem is difficult to handle by the so called curse of dimensionality. To mitigate this issue we apply a reduction of the order by means of a new proper orthogonal decomposition (POD) method based on time derivatives. We carry out the error analysis of the method using recently proved optimal bounds for the fully discrete approximations. Moreover, the use of snapshots based on time derivatives allows us to bound some terms of the error that could not be bounded in a standard POD approach. Some numerical experiments show the good performance of the method in practice.SpringerMatemática Aplicada IIAgencia Estatal de Investigación. EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Junta de Castilla y León2025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/172155https://doi.org/10.1007/s10915-025-02833-0reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Scientific Computing, 103 (1), 19.PID2019-104141GB-I00PID2022-136550NB-I00VA169P20https://link.springer.com/article/10.1007/s10915-025-02833-0info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1721552026-06-17T12:51:07Z
dc.title.none.fl_str_mv Optimal Bounds for POD Approximations of Infinite Horizon Control Problems Based on Time Derivatives
title Optimal Bounds for POD Approximations of Infinite Horizon Control Problems Based on Time Derivatives
spellingShingle Optimal Bounds for POD Approximations of Infinite Horizon Control Problems Based on Time Derivatives
De Frutos, Javier
Dynamic programming
Hamilton–Jacobi–Bellman equation
Optimal control
Proper orthogonal decomposition
Snapshots based on time derivatives
Error analysis
title_short Optimal Bounds for POD Approximations of Infinite Horizon Control Problems Based on Time Derivatives
title_full Optimal Bounds for POD Approximations of Infinite Horizon Control Problems Based on Time Derivatives
title_fullStr Optimal Bounds for POD Approximations of Infinite Horizon Control Problems Based on Time Derivatives
title_full_unstemmed Optimal Bounds for POD Approximations of Infinite Horizon Control Problems Based on Time Derivatives
title_sort Optimal Bounds for POD Approximations of Infinite Horizon Control Problems Based on Time Derivatives
dc.creator.none.fl_str_mv De Frutos, Javier
García-Archilla, Bosco
Novo, Julia
author De Frutos, Javier
author_facet De Frutos, Javier
García-Archilla, Bosco
Novo, Julia
author_role author
author2 García-Archilla, Bosco
Novo, Julia
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada II
Agencia Estatal de Investigación. España
European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
Junta de Castilla y León
dc.subject.none.fl_str_mv Dynamic programming
Hamilton–Jacobi–Bellman equation
Optimal control
Proper orthogonal decomposition
Snapshots based on time derivatives
Error analysis
topic Dynamic programming
Hamilton–Jacobi–Bellman equation
Optimal control
Proper orthogonal decomposition
Snapshots based on time derivatives
Error analysis
description This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/172155
https://doi.org/10.1007/s10915-025-02833-0
url https://hdl.handle.net/11441/172155
https://doi.org/10.1007/s10915-025-02833-0
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Scientific Computing, 103 (1), 19.
PID2019-104141GB-I00
PID2022-136550NB-I00
VA169P20
https://link.springer.com/article/10.1007/s10915-025-02833-0
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
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