Numerical treatment of the bounded-control LQR problem by updating the final phase value

Autores
Costanza, Vicente; Rivadeneira Paz, Pablo Santiago; Gómez Múnera, John Anderson
Año de publicación
2016
Idioma
español castellano
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A novel approach has been developed for approximately solving the constrained LQR problem, based on updating the final state and costate of an unrestricted related regular problem, and the switching times (when the control meets the constraints). The main result is the expression of a suboptimal control in feedback form by using some corresponding Riccati equation. The gradient method is applied to reduce the cost via explicit algebraic formula for its partial derivatives with respect to the hidden final state/costate of the related regular problem. The numerical method results efficient because it does not involve integrations of states or cost trajectories and reduces the dimension of the relevant unknown parameters. All the relevant objects are calculated from a few auxiliary matrices, which are computed only once and kept in memory. The scheme is here applied to the "cheapest stop of a train" case-study whose optimal solution is already known.
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: 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
Fil: Gómez Múnera, John Anderson. 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
Sistemas Lineales
Control Óptimo
Restricciones
Metodo del Gradiente
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:11336/25403
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Numerical treatment of the bounded-control LQR problem by updating the final phase valueCostanza, VicenteRivadeneira Paz, Pablo SantiagoGómez Múnera, John AndersonSistemas LinealesControl ÓptimoRestriccionesMetodo del Gradientehttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2A novel approach has been developed for approximately solving the constrained LQR problem, based on updating the final state and costate of an unrestricted related regular problem, and the switching times (when the control meets the constraints). The main result is the expression of a suboptimal control in feedback form by using some corresponding Riccati equation. The gradient method is applied to reduce the cost via explicit algebraic formula for its partial derivatives with respect to the hidden final state/costate of the related regular problem. The numerical method results efficient because it does not involve integrations of states or cost trajectories and reduces the dimension of the relevant unknown parameters. All the relevant objects are calculated from a few auxiliary matrices, which are computed only once and kept in memory. The scheme is here applied to the "cheapest stop of a train" case-study whose optimal solution is already known.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: 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; ArgentinaFil: Gómez Múnera, John Anderson. 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; ArgentinaInstitute of Electrical and Electronics Engineers2016-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/25403Costanza, Vicente; Rivadeneira Paz, Pablo Santiago; Gómez Múnera, John Anderson; Numerical treatment of the bounded-control LQR problem by updating the final phase value; Institute of Electrical and Electronics Engineers; IEEE Latin America Transactions; 14; 6; 8-2016; 2687-26921548-0992CONICET DigitalCONICETspainfo:eu-repo/semantics/altIdentifier/doi/10.1109/TLA.2016.7555239info:eu-repo/semantics/altIdentifier/url/http://ieeexplore.ieee.org/document/7555239/info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:39:30Zoai:ri.conicet.gov.ar:11336/25403instacron: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 09:39:30.858CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Numerical treatment of the bounded-control LQR problem by updating the final phase value
title Numerical treatment of the bounded-control LQR problem by updating the final phase value
spellingShingle Numerical treatment of the bounded-control LQR problem by updating the final phase value
Costanza, Vicente
Sistemas Lineales
Control Óptimo
Restricciones
Metodo del Gradiente
title_short Numerical treatment of the bounded-control LQR problem by updating the final phase value
title_full Numerical treatment of the bounded-control LQR problem by updating the final phase value
title_fullStr Numerical treatment of the bounded-control LQR problem by updating the final phase value
title_full_unstemmed Numerical treatment of the bounded-control LQR problem by updating the final phase value
title_sort Numerical treatment of the bounded-control LQR problem by updating the final phase value
dc.creator.none.fl_str_mv Costanza, Vicente
Rivadeneira Paz, Pablo Santiago
Gómez Múnera, John Anderson
author Costanza, Vicente
author_facet Costanza, Vicente
Rivadeneira Paz, Pablo Santiago
Gómez Múnera, John Anderson
author_role author
author2 Rivadeneira Paz, Pablo Santiago
Gómez Múnera, John Anderson
author2_role author
author
dc.subject.none.fl_str_mv Sistemas Lineales
Control Óptimo
Restricciones
Metodo del Gradiente
topic Sistemas Lineales
Control Óptimo
Restricciones
Metodo del Gradiente
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv A novel approach has been developed for approximately solving the constrained LQR problem, based on updating the final state and costate of an unrestricted related regular problem, and the switching times (when the control meets the constraints). The main result is the expression of a suboptimal control in feedback form by using some corresponding Riccati equation. The gradient method is applied to reduce the cost via explicit algebraic formula for its partial derivatives with respect to the hidden final state/costate of the related regular problem. The numerical method results efficient because it does not involve integrations of states or cost trajectories and reduces the dimension of the relevant unknown parameters. All the relevant objects are calculated from a few auxiliary matrices, which are computed only once and kept in memory. The scheme is here applied to the "cheapest stop of a train" case-study whose optimal solution is already known.
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: 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
Fil: Gómez Múnera, John Anderson. 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 A novel approach has been developed for approximately solving the constrained LQR problem, based on updating the final state and costate of an unrestricted related regular problem, and the switching times (when the control meets the constraints). The main result is the expression of a suboptimal control in feedback form by using some corresponding Riccati equation. The gradient method is applied to reduce the cost via explicit algebraic formula for its partial derivatives with respect to the hidden final state/costate of the related regular problem. The numerical method results efficient because it does not involve integrations of states or cost trajectories and reduces the dimension of the relevant unknown parameters. All the relevant objects are calculated from a few auxiliary matrices, which are computed only once and kept in memory. The scheme is here applied to the "cheapest stop of a train" case-study whose optimal solution is already known.
publishDate 2016
dc.date.none.fl_str_mv 2016-08
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/11336/25403
Costanza, Vicente; Rivadeneira Paz, Pablo Santiago; Gómez Múnera, John Anderson; Numerical treatment of the bounded-control LQR problem by updating the final phase value; Institute of Electrical and Electronics Engineers; IEEE Latin America Transactions; 14; 6; 8-2016; 2687-2692
1548-0992
CONICET Digital
CONICET
url http://hdl.handle.net/11336/25403
identifier_str_mv Costanza, Vicente; Rivadeneira Paz, Pablo Santiago; Gómez Múnera, John Anderson; Numerical treatment of the bounded-control LQR problem by updating the final phase value; Institute of Electrical and Electronics Engineers; IEEE Latin America Transactions; 14; 6; 8-2016; 2687-2692
1548-0992
CONICET Digital
CONICET
dc.language.none.fl_str_mv spa
language spa
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1109/TLA.2016.7555239
info:eu-repo/semantics/altIdentifier/url/http://ieeexplore.ieee.org/document/7555239/
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
dc.publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers
publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers
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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