Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control Problem

Autores
Costanza, Vicente; Neuman, C. E.
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
New equations involving the unknown final states and initial costates corresponding to families of LQR problems are found, and their solutions are computed and validated. Having the initial values of the costates, the optimal control can then be constructed, for each particular problem, from the solution to the Hamiltonian equations, now achievable through on-line integration. The missing boundary conditions are obtained by solving (offline) two uncoupled, first-order, quasi-linear, partial differential equations for two auxiliary n × n matrices, whose independent variables are the timehorizon duration T and the final-penalty matrix S. The solutions to these PDEs give information on the behavior of the whole two-parameter family of control problems, which can be used for design purposes. The mathematical treatment takes advantage of the symplectic structure of the Hamiltonian formalism, which allows to reformulate one of Bellman's conjectures related to the “invariantimbedding” methodology. Results are tested against solutions of the differential Riccati equations associated with these problems, and the attributes of the two approaches are illustrated and discussed.
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: Neuman, C. E.. Universidad Nacional del Litoral; Argentina
Materia
Optimal Control
Linear-Quadratic Problem
First-Order Pdes
Boundary-Value Problems
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:11336/17096

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network_name_str CONICET Digital (CONICET)
spelling Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control ProblemCostanza, VicenteNeuman, C. E.Optimal ControlLinear-Quadratic ProblemFirst-Order PdesBoundary-Value Problemshttps://purl.org/becyt/ford/2.4https://purl.org/becyt/ford/2New equations involving the unknown final states and initial costates corresponding to families of LQR problems are found, and their solutions are computed and validated. Having the initial values of the costates, the optimal control can then be constructed, for each particular problem, from the solution to the Hamiltonian equations, now achievable through on-line integration. The missing boundary conditions are obtained by solving (offline) two uncoupled, first-order, quasi-linear, partial differential equations for two auxiliary n × n matrices, whose independent variables are the timehorizon duration T and the final-penalty matrix S. The solutions to these PDEs give information on the behavior of the whole two-parameter family of control problems, which can be used for design purposes. The mathematical treatment takes advantage of the symplectic structure of the Hamiltonian formalism, which allows to reformulate one of Bellman's conjectures related to the “invariantimbedding” methodology. Results are tested against solutions of the differential Riccati equations associated with these problems, and the attributes of the two approaches are illustrated and discussed.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: Neuman, C. E.. Universidad Nacional del Litoral; ArgentinaPlanta Piloto de Ingeniería Química2009-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/17096Costanza, Vicente; Neuman, C. E.; Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control Problem; Planta Piloto de Ingeniería Química; Latin American Applied Research; 39; 3; 12-2009; 207-2120327-07931851-8796enginfo:eu-repo/semantics/altIdentifier/url/http://www.laar.uns.edu.ar/indexes/artic_v3903/Vol39_3_207.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:50:36Zoai:ri.conicet.gov.ar:11336/17096instacron: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 09:50:36.665CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control Problem
title Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control Problem
spellingShingle Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control Problem
Costanza, Vicente
Optimal Control
Linear-Quadratic Problem
First-Order Pdes
Boundary-Value Problems
title_short Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control Problem
title_full Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control Problem
title_fullStr Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control Problem
title_full_unstemmed Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control Problem
title_sort Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control Problem
dc.creator.none.fl_str_mv Costanza, Vicente
Neuman, C. E.
author Costanza, Vicente
author_facet Costanza, Vicente
Neuman, C. E.
author_role author
author2 Neuman, C. E.
author2_role author
dc.subject.none.fl_str_mv Optimal Control
Linear-Quadratic Problem
First-Order Pdes
Boundary-Value Problems
topic Optimal Control
Linear-Quadratic Problem
First-Order Pdes
Boundary-Value Problems
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.4
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv New equations involving the unknown final states and initial costates corresponding to families of LQR problems are found, and their solutions are computed and validated. Having the initial values of the costates, the optimal control can then be constructed, for each particular problem, from the solution to the Hamiltonian equations, now achievable through on-line integration. The missing boundary conditions are obtained by solving (offline) two uncoupled, first-order, quasi-linear, partial differential equations for two auxiliary n × n matrices, whose independent variables are the timehorizon duration T and the final-penalty matrix S. The solutions to these PDEs give information on the behavior of the whole two-parameter family of control problems, which can be used for design purposes. The mathematical treatment takes advantage of the symplectic structure of the Hamiltonian formalism, which allows to reformulate one of Bellman's conjectures related to the “invariantimbedding” methodology. Results are tested against solutions of the differential Riccati equations associated with these problems, and the attributes of the two approaches are illustrated and discussed.
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: Neuman, C. E.. Universidad Nacional del Litoral; Argentina
description New equations involving the unknown final states and initial costates corresponding to families of LQR problems are found, and their solutions are computed and validated. Having the initial values of the costates, the optimal control can then be constructed, for each particular problem, from the solution to the Hamiltonian equations, now achievable through on-line integration. The missing boundary conditions are obtained by solving (offline) two uncoupled, first-order, quasi-linear, partial differential equations for two auxiliary n × n matrices, whose independent variables are the timehorizon duration T and the final-penalty matrix S. The solutions to these PDEs give information on the behavior of the whole two-parameter family of control problems, which can be used for design purposes. The mathematical treatment takes advantage of the symplectic structure of the Hamiltonian formalism, which allows to reformulate one of Bellman's conjectures related to the “invariantimbedding” methodology. Results are tested against solutions of the differential Riccati equations associated with these problems, and the attributes of the two approaches are illustrated and discussed.
publishDate 2009
dc.date.none.fl_str_mv 2009-12
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/11336/17096
Costanza, Vicente; Neuman, C. E.; Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control Problem; Planta Piloto de Ingeniería Química; Latin American Applied Research; 39; 3; 12-2009; 207-212
0327-0793
1851-8796
url http://hdl.handle.net/11336/17096
identifier_str_mv Costanza, Vicente; Neuman, C. E.; Partial Differential Equations for Missing Boundary Conditions in the Linear-Quadratic Optimal Control Problem; Planta Piloto de Ingeniería Química; Latin American Applied Research; 39; 3; 12-2009; 207-212
0327-0793
1851-8796
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.laar.uns.edu.ar/indexes/artic_v3903/Vol39_3_207.pdf
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
dc.publisher.none.fl_str_mv Planta Piloto de Ingeniería Química
publisher.none.fl_str_mv Planta Piloto de Ingeniería Química
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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