Averaged control

We analyze the problem of controlling parameter-dependent systems. We introduce the notion of averaged control according to which the quantity of interest is the average of the states with respect to the parameter. First we consider the problem of controllability for linear finite-dimensional system...

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Detalles Bibliográficos
Autor: Zuazua, E.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2014
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/204
Acceso en línea:http://hdl.handle.net/20.500.11824/204
Access Level:acceso abierto
Palabra clave:Optimal controls
Parametrized ODE and PDE
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spelling Averaged controlZuazua, E.Optimal controlsParametrized ODE and PDEWe analyze the problem of controlling parameter-dependent systems. We introduce the notion of averaged control according to which the quantity of interest is the average of the states with respect to the parameter. First we consider the problem of controllability for linear finite-dimensional systems and show that a necessary and sufficient condition for averaged controllability is an averaged rank condition, in the spirit of the classical rank condition for linear control systems, but involving averaged momenta of any order of the matrices generating the dynamics and representing the control action. We also describe some open problems and directions of possible research, in particular on the average controllability of evolution partial differential equations. In this context we analyze also the averaged version of a classical optimal control problem for a parameter dependent elliptic equation and derive the corresponding optimality system.201620162014info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/204reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttp://www.sciencedirect.com/science/article/pii/S000510981400435Xinfo:eu-repo/grantAgreement/EC/FP7/246775info:eu-repo/grantAgreement/MICINN//MTM2011-29306-C02-01info:eu-repo/grantAgreement/MINECO//SEV-2013-0323Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/2042026-06-19T12:47:47Z
dc.title.none.fl_str_mv Averaged control
title Averaged control
spellingShingle Averaged control
Zuazua, E.
Optimal controls
Parametrized ODE and PDE
title_short Averaged control
title_full Averaged control
title_fullStr Averaged control
title_full_unstemmed Averaged control
title_sort Averaged control
dc.creator.none.fl_str_mv Zuazua, E.
author Zuazua, E.
author_facet Zuazua, E.
author_role author
dc.subject.none.fl_str_mv Optimal controls
Parametrized ODE and PDE
topic Optimal controls
Parametrized ODE and PDE
description We analyze the problem of controlling parameter-dependent systems. We introduce the notion of averaged control according to which the quantity of interest is the average of the states with respect to the parameter. First we consider the problem of controllability for linear finite-dimensional systems and show that a necessary and sufficient condition for averaged controllability is an averaged rank condition, in the spirit of the classical rank condition for linear control systems, but involving averaged momenta of any order of the matrices generating the dynamics and representing the control action. We also describe some open problems and directions of possible research, in particular on the average controllability of evolution partial differential equations. In this context we analyze also the averaged version of a classical optimal control problem for a parameter dependent elliptic equation and derive the corresponding optimality system.
publishDate 2014
dc.date.none.fl_str_mv 2014
2016
2016
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url http://hdl.handle.net/20.500.11824/204
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv http://www.sciencedirect.com/science/article/pii/S000510981400435X
info:eu-repo/grantAgreement/EC/FP7/246775
info:eu-repo/grantAgreement/MICINN//MTM2011-29306-C02-01
info:eu-repo/grantAgreement/MINECO//SEV-2013-0323
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
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