Magnus integrators for solving linear-quadratic differential games

We consider Magnus integrators to solve linear-quadratic N-player differential games. These problems require to solve, backward in time, non-autonomous matrix Riccati differential equations which are coupled with the linear differential equations for the dynamic state of the game, to be integrated f...

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Detalles Bibliográficos
Autores: Blanes Zamora, Sergio|||0000-0001-5819-8898, Ponsoda Miralles, Enrique
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/81587
Acceso en línea:https://riunet.upv.es/handle/10251/81587
Access Level:acceso abierto
Palabra clave:Differential games
Coupled Riccati differential equations
Exponential integrators
MATEMATICA APLICADA
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spelling Magnus integrators for solving linear-quadratic differential gamesBlanes Zamora, Sergio|||0000-0001-5819-8898Ponsoda Miralles, EnriqueDifferential gamesCoupled Riccati differential equationsExponential integratorsMATEMATICA APLICADAWe consider Magnus integrators to solve linear-quadratic N-player differential games. These problems require to solve, backward in time, non-autonomous matrix Riccati differential equations which are coupled with the linear differential equations for the dynamic state of the game, to be integrated forward in time. We analyze different Magnus integrators which can provide either analytical or numerical approximations to the equations. They can be considered as time-averaging methods and frequently are used as exponential integrators. We show that they preserve some of the most relevant qualitative properties of the solution for the matrix Riccati differential equations as well as for the remaining equations. The analytical approximations allow us to study the problem in terms of the parameters involved. Some numerical examples are also considered which show that exponential methods are, in general, superior to standard methods.The authors acknowledge the support of the Generalitat Valenciana through the project GV/2009/032. The work of SB has also been partially supported by Ministerio de Ciencia e Innovacion (Spain) under the coordinated project MTM2010-18246-C03 (co-financed by the ERDF of the European Union) and the work of EP has also been partially supported by Ministerio de Ciencia e Innvacion of Spain, by the project MTM2009-08587.ElsevierDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialInstituto Universitario de Matemática MultidisciplinarGeneralitat ValencianaMinisterio de Ciencia e InnovaciónEuropean Regional Development FundRepositorio Institucional de la Universitat Politècnica de València Riunet20122012-08-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/81587reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengGeneralitat Valenciana https://doi.org/10.13039/501100003359 GV%2F2009%2F032 Desarrollo de integradores geométricos adaptados a ecuaciones diferenciales con diferentes escalas de tiempoMinisterio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2010-18246-C03Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2009-08587 Ecuaciones Diferenciales Aleatorias Y Aplicacionesopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/815872026-06-13T07:49:27Z
dc.title.none.fl_str_mv Magnus integrators for solving linear-quadratic differential games
title Magnus integrators for solving linear-quadratic differential games
spellingShingle Magnus integrators for solving linear-quadratic differential games
Blanes Zamora, Sergio|||0000-0001-5819-8898
Differential games
Coupled Riccati differential equations
Exponential integrators
MATEMATICA APLICADA
title_short Magnus integrators for solving linear-quadratic differential games
title_full Magnus integrators for solving linear-quadratic differential games
title_fullStr Magnus integrators for solving linear-quadratic differential games
title_full_unstemmed Magnus integrators for solving linear-quadratic differential games
title_sort Magnus integrators for solving linear-quadratic differential games
dc.creator.none.fl_str_mv Blanes Zamora, Sergio|||0000-0001-5819-8898
Ponsoda Miralles, Enrique
author Blanes Zamora, Sergio|||0000-0001-5819-8898
author_facet Blanes Zamora, Sergio|||0000-0001-5819-8898
Ponsoda Miralles, Enrique
author_role author
author2 Ponsoda Miralles, Enrique
author2_role author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
Instituto Universitario de Matemática Multidisciplinar
Generalitat Valenciana
Ministerio de Ciencia e Innovación
European Regional Development Fund
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Differential games
Coupled Riccati differential equations
Exponential integrators
MATEMATICA APLICADA
topic Differential games
Coupled Riccati differential equations
Exponential integrators
MATEMATICA APLICADA
description We consider Magnus integrators to solve linear-quadratic N-player differential games. These problems require to solve, backward in time, non-autonomous matrix Riccati differential equations which are coupled with the linear differential equations for the dynamic state of the game, to be integrated forward in time. We analyze different Magnus integrators which can provide either analytical or numerical approximations to the equations. They can be considered as time-averaging methods and frequently are used as exponential integrators. We show that they preserve some of the most relevant qualitative properties of the solution for the matrix Riccati differential equations as well as for the remaining equations. The analytical approximations allow us to study the problem in terms of the parameters involved. Some numerical examples are also considered which show that exponential methods are, in general, superior to standard methods.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-08-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
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 https://riunet.upv.es/handle/10251/81587
url https://riunet.upv.es/handle/10251/81587
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Generalitat Valenciana https://doi.org/10.13039/501100003359 GV%2F2009%2F032 Desarrollo de integradores geométricos adaptados a ecuaciones diferenciales con diferentes escalas de tiempo
Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2010-18246-C03
Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2009-08587 Ecuaciones Diferenciales Aleatorias Y Aplicaciones
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
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
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300724

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