Minimizing control energy in a class of bounded-control linear-quadratic regulator problems

Autores
Costanza, Vicente; Rivadeneira Paz, Pablo Santiago; González, Alejandro Hernán
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Minimal-control-energy strategies are substantiated and illustrated for linear-quadratic problems with penalized endpoints and no state-trajectory cost, when bounds in control values are imposed. The optimal solution for a given process with restricted controls, starting at a known initial state, is shown to coincide with the saturated solution to the unrestricted problem that has the same coefficients but starts at a generally different initial state. This result reduces the searching span for the solution: from the infinite-dimensional set of admissible control trajectories to the finite-dimensional Euclidean space of initial conditions. An efficient real-time scheme is proposed here to approximate (eventually to find) the optimal control strategy, based on the detection of the appropriate initial state while avoiding as much as possible the generation and evaluation of state and control trajectories. Numerical (including model predictive control) simulations are provided, compared, and checked against the analytical solution to ‘the cheapest stop of a train’ problem in its pure-upper-bounded brake, flexible-endpoint setting.
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: González, Alejandro Hernán. 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
Optimal Control
Constrained Controls
Linear-Quadratic Problems
Model Predictive Control
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:11336/22364
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Minimizing control energy in a class of bounded-control linear-quadratic regulator problemsCostanza, VicenteRivadeneira Paz, Pablo SantiagoGonzález, Alejandro HernánOptimal ControlConstrained ControlsLinear-Quadratic ProblemsModel Predictive Controlhttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2Minimal-control-energy strategies are substantiated and illustrated for linear-quadratic problems with penalized endpoints and no state-trajectory cost, when bounds in control values are imposed. The optimal solution for a given process with restricted controls, starting at a known initial state, is shown to coincide with the saturated solution to the unrestricted problem that has the same coefficients but starts at a generally different initial state. This result reduces the searching span for the solution: from the infinite-dimensional set of admissible control trajectories to the finite-dimensional Euclidean space of initial conditions. An efficient real-time scheme is proposed here to approximate (eventually to find) the optimal control strategy, based on the detection of the appropriate initial state while avoiding as much as possible the generation and evaluation of state and control trajectories. Numerical (including model predictive control) simulations are provided, compared, and checked against the analytical solution to ‘the cheapest stop of a train’ problem in its pure-upper-bounded brake, flexible-endpoint setting.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: González, Alejandro Hernán. 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; ArgentinaWiley2013-05info: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/11336/22364Costanza, Vicente; Rivadeneira Paz, Pablo Santiago; González, Alejandro Hernán; Minimizing control energy in a class of bounded-control linear-quadratic regulator problems; Wiley; Optimal Control Applications & Methods; 35; 3; 5-2013; 361-3820143-2087CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1002/oca.2072info:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1002/oca.2072/abstractinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:05:47Zoai:ri.conicet.gov.ar:11336/22364instacron: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 10:05:48.105CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Minimizing control energy in a class of bounded-control linear-quadratic regulator problems
title Minimizing control energy in a class of bounded-control linear-quadratic regulator problems
spellingShingle Minimizing control energy in a class of bounded-control linear-quadratic regulator problems
Costanza, Vicente
Optimal Control
Constrained Controls
Linear-Quadratic Problems
Model Predictive Control
title_short Minimizing control energy in a class of bounded-control linear-quadratic regulator problems
title_full Minimizing control energy in a class of bounded-control linear-quadratic regulator problems
title_fullStr Minimizing control energy in a class of bounded-control linear-quadratic regulator problems
title_full_unstemmed Minimizing control energy in a class of bounded-control linear-quadratic regulator problems
title_sort Minimizing control energy in a class of bounded-control linear-quadratic regulator problems
dc.creator.none.fl_str_mv Costanza, Vicente
Rivadeneira Paz, Pablo Santiago
González, Alejandro Hernán
author Costanza, Vicente
author_facet Costanza, Vicente
Rivadeneira Paz, Pablo Santiago
González, Alejandro Hernán
author_role author
author2 Rivadeneira Paz, Pablo Santiago
González, Alejandro Hernán
author2_role author
author
dc.subject.none.fl_str_mv Optimal Control
Constrained Controls
Linear-Quadratic Problems
Model Predictive Control
topic Optimal Control
Constrained Controls
Linear-Quadratic Problems
Model Predictive Control
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv Minimal-control-energy strategies are substantiated and illustrated for linear-quadratic problems with penalized endpoints and no state-trajectory cost, when bounds in control values are imposed. The optimal solution for a given process with restricted controls, starting at a known initial state, is shown to coincide with the saturated solution to the unrestricted problem that has the same coefficients but starts at a generally different initial state. This result reduces the searching span for the solution: from the infinite-dimensional set of admissible control trajectories to the finite-dimensional Euclidean space of initial conditions. An efficient real-time scheme is proposed here to approximate (eventually to find) the optimal control strategy, based on the detection of the appropriate initial state while avoiding as much as possible the generation and evaluation of state and control trajectories. Numerical (including model predictive control) simulations are provided, compared, and checked against the analytical solution to ‘the cheapest stop of a train’ problem in its pure-upper-bounded brake, flexible-endpoint setting.
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: González, Alejandro Hernán. 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 Minimal-control-energy strategies are substantiated and illustrated for linear-quadratic problems with penalized endpoints and no state-trajectory cost, when bounds in control values are imposed. The optimal solution for a given process with restricted controls, starting at a known initial state, is shown to coincide with the saturated solution to the unrestricted problem that has the same coefficients but starts at a generally different initial state. This result reduces the searching span for the solution: from the infinite-dimensional set of admissible control trajectories to the finite-dimensional Euclidean space of initial conditions. An efficient real-time scheme is proposed here to approximate (eventually to find) the optimal control strategy, based on the detection of the appropriate initial state while avoiding as much as possible the generation and evaluation of state and control trajectories. Numerical (including model predictive control) simulations are provided, compared, and checked against the analytical solution to ‘the cheapest stop of a train’ problem in its pure-upper-bounded brake, flexible-endpoint setting.
publishDate 2013
dc.date.none.fl_str_mv 2013-05
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/11336/22364
Costanza, Vicente; Rivadeneira Paz, Pablo Santiago; González, Alejandro Hernán; Minimizing control energy in a class of bounded-control linear-quadratic regulator problems; Wiley; Optimal Control Applications & Methods; 35; 3; 5-2013; 361-382
0143-2087
CONICET Digital
CONICET
url http://hdl.handle.net/11336/22364
identifier_str_mv Costanza, Vicente; Rivadeneira Paz, Pablo Santiago; González, Alejandro Hernán; Minimizing control energy in a class of bounded-control linear-quadratic regulator problems; Wiley; Optimal Control Applications & Methods; 35; 3; 5-2013; 361-382
0143-2087
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1002/oca.2072
info:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1002/oca.2072/abstract
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 Wiley
publisher.none.fl_str_mv Wiley
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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