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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/63503
Ver los metadatos del registro completo
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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 Técnicas2025-09-03T10:05:15Zoai: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:34982025-09-03 10:05:15.632CONICET 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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1842269901509623808 |
score |
13.13397 |