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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/22364
Ver los metadatos del registro completo
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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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1844613898070654976 |
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13.070432 |