Actuator design for parabolic distributed parameter systems with the moment method

First Published in SIAM Journal on Control and Optimization in Volume 55, Issue 2, 2017, Pages 1128-1152, published by the Society for Industrial and Applied Mathematics (SIAM)

Detalhes bibliográficos
Autores: Privat, Yannick, Trelat, Emmanuel, Zuazua Iriondo, Enrique
Formato: artículo
Fecha de publicación:2017
País:España
Recursos:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/688103
Acesso em linha:http://hdl.handle.net/10486/688103
https://dx.doi.org/10.1137/16M1058418
Access Level:acceso abierto
Palavra-chave:Heat equation
Lumped control
Moment method
Null controllability
Parabolic systems
Shape optimization
Matemáticas
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spelling Actuator design for parabolic distributed parameter systems with the moment methodPrivat, YannickTrelat, EmmanuelZuazua Iriondo, EnriqueHeat equationLumped controlMoment methodNull controllabilityParabolic systemsShape optimizationMatemáticasFirst Published in SIAM Journal on Control and Optimization in Volume 55, Issue 2, 2017, Pages 1128-1152, published by the Society for Industrial and Applied Mathematics (SIAM)In this paper, we model and solve the problem of designing in an optimal way actuators for parabolic partial differential equations settled on a bounded open connected subset of Rn. We optimize not only the location but also the shape of actuators, by finding what is the optimal distribution of actuators in , over all possible such distributions of a given measure. Using the moment method, we formulate a spectral optimal design problem, which consists of maximizing a criterion corresponding to an average over random initial data of the largest L2-energy of controllers. Since we choose the moment method to control the PDE, our study mainly covers one-dimensional parabolic operators, but we also provide several examples in higher dimensions. We consider two types of controllers: Either internal controls, modeled by characteristic functions, or lumped controls, that are tensorized functions in time and space. Under appropriate spectral assumptions, we prove existence and uniqueness of an optimal actuator distribution, and we provide a simple computation procedure. Numerical simulations illustrate our resultsThe first author was partially supported by ANR project OPTIFORM. This work was partially supported by Advanced Grant DYCON (Dynamic Control) of the European Research Council Executive Agency, GA 694126, ICON of the French ANR-2016-ACHN-0014-01, FA9550-15-1-0027 of AFOSR, A9550-14-1-0214 of EOARD-AFOSR, and grant MTM2014-52347 of MINECO (Spain)Society for Industrial and Applied MathematicsDepartamento de MatemáticasFacultad de Ciencias20172017-04-06research articlehttp://purl.org/coar/resource_type/c_2df8fbb1VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/688103https://dx.doi.org/10.1137/16M1058418reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengEuropean Commission http://dx.doi.org/10.13039/501100000780 Horizon 2020 Framework Programme 694126open accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/6881032026-06-23T12:46:27Z
dc.title.none.fl_str_mv Actuator design for parabolic distributed parameter systems with the moment method
title Actuator design for parabolic distributed parameter systems with the moment method
spellingShingle Actuator design for parabolic distributed parameter systems with the moment method
Privat, Yannick
Heat equation
Lumped control
Moment method
Null controllability
Parabolic systems
Shape optimization
Matemáticas
title_short Actuator design for parabolic distributed parameter systems with the moment method
title_full Actuator design for parabolic distributed parameter systems with the moment method
title_fullStr Actuator design for parabolic distributed parameter systems with the moment method
title_full_unstemmed Actuator design for parabolic distributed parameter systems with the moment method
title_sort Actuator design for parabolic distributed parameter systems with the moment method
dc.creator.none.fl_str_mv Privat, Yannick
Trelat, Emmanuel
Zuazua Iriondo, Enrique
author Privat, Yannick
author_facet Privat, Yannick
Trelat, Emmanuel
Zuazua Iriondo, Enrique
author_role author
author2 Trelat, Emmanuel
Zuazua Iriondo, Enrique
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Heat equation
Lumped control
Moment method
Null controllability
Parabolic systems
Shape optimization
Matemáticas
topic Heat equation
Lumped control
Moment method
Null controllability
Parabolic systems
Shape optimization
Matemáticas
description First Published in SIAM Journal on Control and Optimization in Volume 55, Issue 2, 2017, Pages 1128-1152, published by the Society for Industrial and Applied Mathematics (SIAM)
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-04-06
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/10486/688103
https://dx.doi.org/10.1137/16M1058418
url http://hdl.handle.net/10486/688103
https://dx.doi.org/10.1137/16M1058418
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission http://dx.doi.org/10.13039/501100000780 Horizon 2020 Framework Programme 694126
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.format.none.fl_str_mv application/pdf
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 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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score 15.300719

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