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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/17096
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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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1844613559034576896 |
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13.070432 |