Approximating the Solution to LQR Problems with Bounded Controls

Autores
Costanza, Vicente; Rivadeneira Paz, Pablo Santiago
Año de publicación
2011
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 shown to be useful in calculating optimal strategies when bounded control restrictions are present, and in approximating the solution to fixed-end problems. The missing boundary values of the Hamiltonian equations are obtained by (off-line) solving two uncoupled, first-order, linear partial differential equations for two auxiliary n×n matrices, whose independent variables are the time-horizon duration T and the eigenvalues of the final-penalty matrix S. The solutions to these PDEs give information on the behavior of the whole (T,S)-family of control problems.  Illustrations of numerical results are provided and checked against analytical solutions of  ´the cheapest stop of a train´ problem.
Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina
Fil: Rivadeneira Paz, Pablo Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina
Materia
Optimal Control
Constrained Control
Lqr
First Order Pdes
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:11336/13105
Acceder
id CONICETDig_04ece3d287329d6854f825ed27e2ea7d
oai_identifier_str oai:ri.conicet.gov.ar:11336/13105
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Approximating the Solution to LQR Problems with Bounded ControlsCostanza, VicenteRivadeneira Paz, Pablo SantiagoOptimal ControlConstrained ControlLqrFirst Order Pdeshttps://purl.org/becyt/ford/2.11https://purl.org/becyt/ford/2New equations involving the unknown final states and initial costates corresponding to families of LQR problems are shown to be useful in calculating optimal strategies when bounded control restrictions are present, and in approximating the solution to fixed-end problems. The missing boundary values of the Hamiltonian equations are obtained by (off-line) solving two uncoupled, first-order, linear partial differential equations for two auxiliary n×n matrices, whose independent variables are the time-horizon duration T and the eigenvalues of the final-penalty matrix S. The solutions to these PDEs give information on the behavior of the whole (T,S)-family of control problems.  Illustrations of numerical results are provided and checked against analytical solutions of  ´the cheapest stop of a train´ problem.Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); ArgentinaFil: Rivadeneira Paz, Pablo Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); ArgentinaPlanta Piloto de Ingeniería Química2011-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/13105Costanza, Vicente; Rivadeneira Paz, Pablo Santiago; Approximating the Solution to LQR Problems with Bounded Controls; Planta Piloto de Ingeniería Química; Latin American Applied Research; 41; 4; 8-2011; 339-3510327-07931851-8796enginfo:eu-repo/semantics/altIdentifier/url/http://ref.scielo.org/2458jhinfo:eu-repo/semantics/altIdentifier/url/http://www.laar.uns.edu.ar/indexes/artic_v4104/Vol41_04_339.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 Técnicas2025-09-03T10:09:35Zoai:ri.conicet.gov.ar:11336/13105instacron: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:34982025-09-03 10:09:35.783CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Approximating the Solution to LQR Problems with Bounded Controls
title Approximating the Solution to LQR Problems with Bounded Controls
spellingShingle Approximating the Solution to LQR Problems with Bounded Controls
Costanza, Vicente
Optimal Control
Constrained Control
Lqr
First Order Pdes
title_short Approximating the Solution to LQR Problems with Bounded Controls
title_full Approximating the Solution to LQR Problems with Bounded Controls
title_fullStr Approximating the Solution to LQR Problems with Bounded Controls
title_full_unstemmed Approximating the Solution to LQR Problems with Bounded Controls
title_sort Approximating the Solution to LQR Problems with Bounded Controls
dc.creator.none.fl_str_mv Costanza, Vicente
Rivadeneira Paz, Pablo Santiago
author Costanza, Vicente
author_facet Costanza, Vicente
Rivadeneira Paz, Pablo Santiago
author_role author
author2 Rivadeneira Paz, Pablo Santiago
author2_role author
dc.subject.none.fl_str_mv Optimal Control
Constrained Control
Lqr
First Order Pdes
topic Optimal Control
Constrained Control
Lqr
First Order Pdes
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.11
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 shown to be useful in calculating optimal strategies when bounded control restrictions are present, and in approximating the solution to fixed-end problems. The missing boundary values of the Hamiltonian equations are obtained by (off-line) solving two uncoupled, first-order, linear partial differential equations for two auxiliary n×n matrices, whose independent variables are the time-horizon duration T and the eigenvalues of the final-penalty matrix S. The solutions to these PDEs give information on the behavior of the whole (T,S)-family of control problems.  Illustrations of numerical results are provided and checked against analytical solutions of  ´the cheapest stop of a train´ problem.
Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina
Fil: Rivadeneira Paz, Pablo Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina
description New equations involving the unknown final states and initial costates corresponding to families of LQR problems are shown to be useful in calculating optimal strategies when bounded control restrictions are present, and in approximating the solution to fixed-end problems. The missing boundary values of the Hamiltonian equations are obtained by (off-line) solving two uncoupled, first-order, linear partial differential equations for two auxiliary n×n matrices, whose independent variables are the time-horizon duration T and the eigenvalues of the final-penalty matrix S. The solutions to these PDEs give information on the behavior of the whole (T,S)-family of control problems.  Illustrations of numerical results are provided and checked against analytical solutions of  ´the cheapest stop of a train´ problem.
publishDate 2011
dc.date.none.fl_str_mv 2011-08
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/11336/13105
Costanza, Vicente; Rivadeneira Paz, Pablo Santiago; Approximating the Solution to LQR Problems with Bounded Controls; Planta Piloto de Ingeniería Química; Latin American Applied Research; 41; 4; 8-2011; 339-351
0327-0793
1851-8796
url http://hdl.handle.net/11336/13105
identifier_str_mv Costanza, Vicente; Rivadeneira Paz, Pablo Santiago; Approximating the Solution to LQR Problems with Bounded Controls; Planta Piloto de Ingeniería Química; Latin American Applied Research; 41; 4; 8-2011; 339-351
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://ref.scielo.org/2458jh
info:eu-repo/semantics/altIdentifier/url/http://www.laar.uns.edu.ar/indexes/artic_v4104/Vol41_04_339.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
_version_ 1842270087387545600
score 13.13397

Publicaciones similares