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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| 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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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 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion |
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article |
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acceptedVersion |
| dc.identifier.none.fl_str_mv |
http://hdl.handle.net/20.500.11824/204 |
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http://hdl.handle.net/20.500.11824/204 |
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Inglés |
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Inglés |
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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 |
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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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Reconocimiento-NoComercial-CompartirIgual 3.0 España http://creativecommons.org/licenses/by-nc-sa/3.0/es/ |
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openAccess |
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application/pdf |
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reponame:BIRD. BCAM's Institutional Repository Data instname:Basque Center for Applied Mathematics (BCAM) |
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Basque Center for Applied Mathematics (BCAM) |
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BIRD. BCAM's Institutional Repository Data |
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BIRD. BCAM's Institutional Repository Data |
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1869407636245446656 |
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15.301603 |