A cost reduction procedure for control-restricted nonlinear systems

Autores
Gómez Múnera, John Anderson; Rivadeneira Paz, Pablo Santiago; Costanza, Vicente
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper describes a numerical scheme to approximate the solution of the optimal control problem for nonlinear systems with restrictions on the manipulated variables. The method proposed here systematically reduces the cost associated with successively updated control strategies after proposing an initial seed trajectory. It follows two main lines of reasoning, the first one relying on linearizations around a seed state/control trajectory and exploiting a theoretical expression for the increment of the cost. This setup is valid in regular situations, and it can be used when saturations occur after some adaptations. One of its advantages is that the decreasing of the cost can be assessed without integrating numerically the nonlinear dynamics. However, and because of the constraints, eventually this method fails, and an alternative approach must be activated to continue decreasing the cost. The alternative approach is based on specific control variations of the current control strategy, and it is activated depending on two theoretical criteria (failure alert) developed here. The first control variation proposed is derived from the differential Riccati equation for the linearized system and appropriate quadratic cost functions. Other variations, similar to those used in Pontryagin theorem for generating the final cone of states, are proposed by modifying the locations of ‘switching times’, producing oscillations in the interior of regular periods. The performance of the numerical proposed method and the related mathematical objects are illustrated by optimizing two-dimensional nonlinear systems with a scalar bounded control.
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
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: 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
Materia
CONTROL VARIATIONS
LQR PROBLEMS
NONLINEAR SYSTEMS
OPTIMAL CONTROL
RESTRICTED CONTROLS
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:11336/63503
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/63503
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A cost reduction procedure for control-restricted nonlinear systemsGómez Múnera, John AndersonRivadeneira Paz, Pablo SantiagoCostanza, VicenteCONTROL VARIATIONSLQR PROBLEMSNONLINEAR SYSTEMSOPTIMAL CONTROLRESTRICTED CONTROLShttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This paper describes a numerical scheme to approximate the solution of the optimal control problem for nonlinear systems with restrictions on the manipulated variables. The method proposed here systematically reduces the cost associated with successively updated control strategies after proposing an initial seed trajectory. It follows two main lines of reasoning, the first one relying on linearizations around a seed state/control trajectory and exploiting a theoretical expression for the increment of the cost. This setup is valid in regular situations, and it can be used when saturations occur after some adaptations. One of its advantages is that the decreasing of the cost can be assessed without integrating numerically the nonlinear dynamics. However, and because of the constraints, eventually this method fails, and an alternative approach must be activated to continue decreasing the cost. The alternative approach is based on specific control variations of the current control strategy, and it is activated depending on two theoretical criteria (failure alert) developed here. The first control variation proposed is derived from the differential Riccati equation for the linearized system and appropriate quadratic cost functions. Other variations, similar to those used in Pontryagin theorem for generating the final cone of states, are proposed by modifying the locations of ‘switching times’, producing oscillations in the interior of regular periods. The performance of the numerical proposed method and the related mathematical objects are illustrated by optimizing two-dimensional nonlinear systems with a scalar bounded control.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; 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: 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; ArgentinaPraise Worthy Prize2017-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/63503Gómez Múnera, John Anderson; Rivadeneira Paz, Pablo Santiago; Costanza, Vicente; A cost reduction procedure for control-restricted nonlinear systems; Praise Worthy Prize; International Review of Automatic Control; 10; 6; 11-2017; 510-5221974-6059CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.15866/ireaco.v10i6.13820info:eu-repo/semantics/altIdentifier/url/https://www.praiseworthyprize.org/jsm/index.php?journal=ireaco&page=article&op=view&path[]=21623info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:26:02Zoai:ri.conicet.gov.ar:11336/63503instacron: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 10:26:02.462CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A cost reduction procedure for control-restricted nonlinear systems
title A cost reduction procedure for control-restricted nonlinear systems
spellingShingle A cost reduction procedure for control-restricted nonlinear systems
Gómez Múnera, John Anderson
CONTROL VARIATIONS
LQR PROBLEMS
NONLINEAR SYSTEMS
OPTIMAL CONTROL
RESTRICTED CONTROLS
title_short A cost reduction procedure for control-restricted nonlinear systems
title_full A cost reduction procedure for control-restricted nonlinear systems
title_fullStr A cost reduction procedure for control-restricted nonlinear systems
title_full_unstemmed A cost reduction procedure for control-restricted nonlinear systems
title_sort A cost reduction procedure for control-restricted nonlinear systems
dc.creator.none.fl_str_mv Gómez Múnera, John Anderson
Rivadeneira Paz, Pablo Santiago
Costanza, Vicente
author Gómez Múnera, John Anderson
author_facet Gómez Múnera, John Anderson
Rivadeneira Paz, Pablo Santiago
Costanza, Vicente
author_role author
author2 Rivadeneira Paz, Pablo Santiago
Costanza, Vicente
author2_role author
author
dc.subject.none.fl_str_mv CONTROL VARIATIONS
LQR PROBLEMS
NONLINEAR SYSTEMS
OPTIMAL CONTROL
RESTRICTED CONTROLS
topic CONTROL VARIATIONS
LQR PROBLEMS
NONLINEAR SYSTEMS
OPTIMAL CONTROL
RESTRICTED CONTROLS
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This paper describes a numerical scheme to approximate the solution of the optimal control problem for nonlinear systems with restrictions on the manipulated variables. The method proposed here systematically reduces the cost associated with successively updated control strategies after proposing an initial seed trajectory. It follows two main lines of reasoning, the first one relying on linearizations around a seed state/control trajectory and exploiting a theoretical expression for the increment of the cost. This setup is valid in regular situations, and it can be used when saturations occur after some adaptations. One of its advantages is that the decreasing of the cost can be assessed without integrating numerically the nonlinear dynamics. However, and because of the constraints, eventually this method fails, and an alternative approach must be activated to continue decreasing the cost. The alternative approach is based on specific control variations of the current control strategy, and it is activated depending on two theoretical criteria (failure alert) developed here. The first control variation proposed is derived from the differential Riccati equation for the linearized system and appropriate quadratic cost functions. Other variations, similar to those used in Pontryagin theorem for generating the final cone of states, are proposed by modifying the locations of ‘switching times’, producing oscillations in the interior of regular periods. The performance of the numerical proposed method and the related mathematical objects are illustrated by optimizing two-dimensional nonlinear systems with a scalar bounded control.
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
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: 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
description This paper describes a numerical scheme to approximate the solution of the optimal control problem for nonlinear systems with restrictions on the manipulated variables. The method proposed here systematically reduces the cost associated with successively updated control strategies after proposing an initial seed trajectory. It follows two main lines of reasoning, the first one relying on linearizations around a seed state/control trajectory and exploiting a theoretical expression for the increment of the cost. This setup is valid in regular situations, and it can be used when saturations occur after some adaptations. One of its advantages is that the decreasing of the cost can be assessed without integrating numerically the nonlinear dynamics. However, and because of the constraints, eventually this method fails, and an alternative approach must be activated to continue decreasing the cost. The alternative approach is based on specific control variations of the current control strategy, and it is activated depending on two theoretical criteria (failure alert) developed here. The first control variation proposed is derived from the differential Riccati equation for the linearized system and appropriate quadratic cost functions. Other variations, similar to those used in Pontryagin theorem for generating the final cone of states, are proposed by modifying the locations of ‘switching times’, producing oscillations in the interior of regular periods. The performance of the numerical proposed method and the related mathematical objects are illustrated by optimizing two-dimensional nonlinear systems with a scalar bounded control.
publishDate 2017
dc.date.none.fl_str_mv 2017-11
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/11336/63503
Gómez Múnera, John Anderson; Rivadeneira Paz, Pablo Santiago; Costanza, Vicente; A cost reduction procedure for control-restricted nonlinear systems; Praise Worthy Prize; International Review of Automatic Control; 10; 6; 11-2017; 510-522
1974-6059
CONICET Digital
CONICET
url http://hdl.handle.net/11336/63503
identifier_str_mv Gómez Múnera, John Anderson; Rivadeneira Paz, Pablo Santiago; Costanza, Vicente; A cost reduction procedure for control-restricted nonlinear systems; Praise Worthy Prize; International Review of Automatic Control; 10; 6; 11-2017; 510-522
1974-6059
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.15866/ireaco.v10i6.13820
info:eu-repo/semantics/altIdentifier/url/https://www.praiseworthyprize.org/jsm/index.php?journal=ireaco&page=article&op=view&path[]=21623
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
application/pdf
dc.publisher.none.fl_str_mv Praise Worthy Prize
publisher.none.fl_str_mv Praise Worthy Prize
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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