Numerical Solution of the Variational PDEs Arising in Optimal Control Theory

Autores
Costanza, Vicente; Troparevski, M. I.; Rivadeneira Paz, Pablo Santiago
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
An iterative method based on Picard’s approach to ODEs’ initial-value problems is proposed to solve first-order quasilinear PDEs with matrix-valued unknowns, in particular, the recently discovered variational PDEs for the missing boundary values in Hamilton equations of optimal control. As illustrations the iterative numerical solutions are checked against the analytical solutions to some examples arising from optimal control problems for nonlinear systems and regular Lagrangians in nite dimension, and against the numerical solution obtained through standard mathematical software. An application tothe (n+1)-dimensional variational PDEs associated with the n-dimensional finite-horizon time-variant linear-quadratic problem is discussed, due to the key role the LQR plays in two-degrees-of freedom control strategies for nonlinear systems with generalized costs.
Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina
Fil: Troparevski, M. I.. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina
Fil: Rivadeneira Paz, Pablo Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina
Materia
Numerical methods for first-order PDEs
Hamiltonian equations
optimal control
nonlinear systems
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/246039
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Numerical Solution of the Variational PDEs Arising in Optimal Control TheoryCostanza, VicenteTroparevski, M. I.Rivadeneira Paz, Pablo SantiagoNumerical methods for first-order PDEsHamiltonian equationsoptimal controlnonlinear systemshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1An iterative method based on Picard’s approach to ODEs’ initial-value problems is proposed to solve first-order quasilinear PDEs with matrix-valued unknowns, in particular, the recently discovered variational PDEs for the missing boundary values in Hamilton equations of optimal control. As illustrations the iterative numerical solutions are checked against the analytical solutions to some examples arising from optimal control problems for nonlinear systems and regular Lagrangians in nite dimension, and against the numerical solution obtained through standard mathematical software. An application tothe (n+1)-dimensional variational PDEs associated with the n-dimensional finite-horizon time-variant linear-quadratic problem is discussed, due to the key role the LQR plays in two-degrees-of freedom control strategies for nonlinear systems with generalized costs.Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Troparevski, M. I.. Universidad de Buenos Aires. Facultad de Ingeniería; ArgentinaFil: Rivadeneira Paz, Pablo Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaICMC/USP - SBMAC2012-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/246039Costanza, Vicente; Troparevski, M. I.; Rivadeneira Paz, Pablo Santiago; Numerical Solution of the Variational PDEs Arising in Optimal Control Theory; ICMC/USP - SBMAC; Computational And Applied Mathematics; 31; 1; 4-2012; 37-580101-8205CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.scielo.br/j/cam/a/pw6Vrkk4N95pqTkwR4Lr9By/?lang=eninfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:03:51Zoai:ri.conicet.gov.ar:11336/246039instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:03:52.24CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Numerical Solution of the Variational PDEs Arising in Optimal Control Theory
title Numerical Solution of the Variational PDEs Arising in Optimal Control Theory
spellingShingle Numerical Solution of the Variational PDEs Arising in Optimal Control Theory
Costanza, Vicente
Numerical methods for first-order PDEs
Hamiltonian equations
optimal control
nonlinear systems
title_short Numerical Solution of the Variational PDEs Arising in Optimal Control Theory
title_full Numerical Solution of the Variational PDEs Arising in Optimal Control Theory
title_fullStr Numerical Solution of the Variational PDEs Arising in Optimal Control Theory
title_full_unstemmed Numerical Solution of the Variational PDEs Arising in Optimal Control Theory
title_sort Numerical Solution of the Variational PDEs Arising in Optimal Control Theory
dc.creator.none.fl_str_mv Costanza, Vicente
Troparevski, M. I.
Rivadeneira Paz, Pablo Santiago
author Costanza, Vicente
author_facet Costanza, Vicente
Troparevski, M. I.
Rivadeneira Paz, Pablo Santiago
author_role author
author2 Troparevski, M. I.
Rivadeneira Paz, Pablo Santiago
author2_role author
author
dc.subject.none.fl_str_mv Numerical methods for first-order PDEs
Hamiltonian equations
optimal control
nonlinear systems
topic Numerical methods for first-order PDEs
Hamiltonian equations
optimal control
nonlinear systems
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv An iterative method based on Picard’s approach to ODEs’ initial-value problems is proposed to solve first-order quasilinear PDEs with matrix-valued unknowns, in particular, the recently discovered variational PDEs for the missing boundary values in Hamilton equations of optimal control. As illustrations the iterative numerical solutions are checked against the analytical solutions to some examples arising from optimal control problems for nonlinear systems and regular Lagrangians in nite dimension, and against the numerical solution obtained through standard mathematical software. An application tothe (n+1)-dimensional variational PDEs associated with the n-dimensional finite-horizon time-variant linear-quadratic problem is discussed, due to the key role the LQR plays in two-degrees-of freedom control strategies for nonlinear systems with generalized costs.
Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina
Fil: Troparevski, M. I.. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina
Fil: Rivadeneira Paz, Pablo Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina
description An iterative method based on Picard’s approach to ODEs’ initial-value problems is proposed to solve first-order quasilinear PDEs with matrix-valued unknowns, in particular, the recently discovered variational PDEs for the missing boundary values in Hamilton equations of optimal control. As illustrations the iterative numerical solutions are checked against the analytical solutions to some examples arising from optimal control problems for nonlinear systems and regular Lagrangians in nite dimension, and against the numerical solution obtained through standard mathematical software. An application tothe (n+1)-dimensional variational PDEs associated with the n-dimensional finite-horizon time-variant linear-quadratic problem is discussed, due to the key role the LQR plays in two-degrees-of freedom control strategies for nonlinear systems with generalized costs.
publishDate 2012
dc.date.none.fl_str_mv 2012-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/246039
Costanza, Vicente; Troparevski, M. I.; Rivadeneira Paz, Pablo Santiago; Numerical Solution of the Variational PDEs Arising in Optimal Control Theory; ICMC/USP - SBMAC; Computational And Applied Mathematics; 31; 1; 4-2012; 37-58
0101-8205
CONICET Digital
CONICET
url http://hdl.handle.net/11336/246039
identifier_str_mv Costanza, Vicente; Troparevski, M. I.; Rivadeneira Paz, Pablo Santiago; Numerical Solution of the Variational PDEs Arising in Optimal Control Theory; ICMC/USP - SBMAC; Computational And Applied Mathematics; 31; 1; 4-2012; 37-58
0101-8205
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.scielo.br/j/cam/a/pw6Vrkk4N95pqTkwR4Lr9By/?lang=en
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv ICMC/USP - SBMAC
publisher.none.fl_str_mv ICMC/USP - SBMAC
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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