Uniform turnpike property and singular limits

Motivated by singular limits for long-time optimal control problems, we investigate a class of parameter-dependent parabolic equations. First, we prove a turnpike result, uniform with respect to the parameters within a suitable regularity class and under appropriate bounds. The main ingredient of ou...

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Bibliographic Details
Authors: Hernández, Martín, Zuazua Iriondo, Enrique
Format: article
Publication Date:2024
Country:España
Institution:Universidad Autónoma de Madrid
Repository:Biblos-e Archivo. Repositorio Institucional de la UAM
Language:English
OAI Identifier:oai:repositorio.uam.es:10486/713693
Online Access:http://hdl.handle.net/10486/713693
https://dx.doi.org/10.1007/s10440-024-00640-7
Access Level:Open access
Keyword:Turnpike property
rapidly oscillating linear parabolic equation
optimal control problems
long time behavior
uniform controllability
singular limits problems
Matemáticas
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spelling Uniform turnpike property and singular limitsHernández, MartínZuazua Iriondo, EnriqueTurnpike propertyrapidly oscillating linear parabolic equationoptimal control problemslong time behavioruniform controllabilitysingular limits problemsMatemáticasMotivated by singular limits for long-time optimal control problems, we investigate a class of parameter-dependent parabolic equations. First, we prove a turnpike result, uniform with respect to the parameters within a suitable regularity class and under appropriate bounds. The main ingredient of our proof is the justification of the uniform exponential stabilization of the corresponding Riccati equations, which is derived from the uniform null control properties of the model. Then, we focus on a heat equation with rapidly oscillating coefficients. In the one-dimensional setting, we obtain a uniform turnpike property with respect to the highly oscillatory heterogeneous medium. Afterward, we establish the homogenization of the turnpike property. Finally, our results are validated by numerical experimentsM. Hernandez has been funded by the Transregio 154 Project, “Mathematical Modelling, Simulation, and Optimization Using the Example of Gas Networks” of the DFG, project C07, and the fellowship “ANID-DAAD bilateral agreement” 57600326. E. Zuazua has been funded by the Alexander von Humboldt-Professorship program, the ModConFlex Marie Curie Action, HORIZON-MSCA-2021-DN-01, the COST Action MAT-DYN-NET, the Transregio 154 Project “Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks” of the DFG, grants PID2020-112617GB-C22 and TED2021-131390B-I00 of MINECO (Spain). Madrid Government - UAM Agreement for the Excellence of the University Research Staff in the context of the V PRICIT (Regional Programme of Research and Technological Innovation)SpringerDepartamento de MatemáticasFacultad de Ciencias20242024-03-24research articlehttp://purl.org/coar/resource_type/c_2df8fbb1VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/713693https://dx.doi.org/10.1007/s10440-024-00640-7reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/7136932026-06-23T12:46:27Z
dc.title.none.fl_str_mv Uniform turnpike property and singular limits
title Uniform turnpike property and singular limits
spellingShingle Uniform turnpike property and singular limits
Hernández, Martín
Turnpike property
rapidly oscillating linear parabolic equation
optimal control problems
long time behavior
uniform controllability
singular limits problems
Matemáticas
title_short Uniform turnpike property and singular limits
title_full Uniform turnpike property and singular limits
title_fullStr Uniform turnpike property and singular limits
title_full_unstemmed Uniform turnpike property and singular limits
title_sort Uniform turnpike property and singular limits
dc.creator.none.fl_str_mv Hernández, Martín
Zuazua Iriondo, Enrique
author Hernández, Martín
author_facet Hernández, Martín
Zuazua Iriondo, Enrique
author_role author
author2 Zuazua Iriondo, Enrique
author2_role author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Turnpike property
rapidly oscillating linear parabolic equation
optimal control problems
long time behavior
uniform controllability
singular limits problems
Matemáticas
topic Turnpike property
rapidly oscillating linear parabolic equation
optimal control problems
long time behavior
uniform controllability
singular limits problems
Matemáticas
description Motivated by singular limits for long-time optimal control problems, we investigate a class of parameter-dependent parabolic equations. First, we prove a turnpike result, uniform with respect to the parameters within a suitable regularity class and under appropriate bounds. The main ingredient of our proof is the justification of the uniform exponential stabilization of the corresponding Riccati equations, which is derived from the uniform null control properties of the model. Then, we focus on a heat equation with rapidly oscillating coefficients. In the one-dimensional setting, we obtain a uniform turnpike property with respect to the highly oscillatory heterogeneous medium. Afterward, we establish the homogenization of the turnpike property. Finally, our results are validated by numerical experiments
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-03-24
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10486/713693
https://dx.doi.org/10.1007/s10440-024-00640-7
url http://hdl.handle.net/10486/713693
https://dx.doi.org/10.1007/s10440-024-00640-7
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
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
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
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
repository.name.fl_str_mv
repository.mail.fl_str_mv
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