Estimation of domains of attraction: A global optimization approach

Autores
Matallana Perez, Luis Geronimo; Blanco, Anibal Manuel; Bandoni, Jose Alberto
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper a methodology for the estimation of domains of attraction of stable equilibriums based on maximal Lyapunov functions is proposed. The basic idea consists in finding the best level set of a Lyapunov function which is fully contained in the region of negative definiteness of its time derivative. An optimization problem is formulated, which includes a tangency requirement between the level sets and constraints on the sign of the numerator and denominator of the Lyapunov function. Such constraints help in avoiding a large number of potential dummy solutions of the nonlinear optimization model. Moreover, since global optimality is also required for proper estimation, a deterministic global optimization solver of the branch and bound type is adopted. The methodology is applied to several examples to illustrate different aspects of the approach.
Fil: Matallana Perez, Luis Geronimo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentina
Fil: Blanco, Anibal Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentina
Fil: Bandoni, Jose Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentina
Materia
DOMAINS OF ATTRACTION
GLOBAL OPTIMIZATION
LYAPUNOV FUNCTION
NONLINEAR DYNAMIC SYSTEMS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/55939
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Estimation of domains of attraction: A global optimization approachMatallana Perez, Luis GeronimoBlanco, Anibal ManuelBandoni, Jose AlbertoDOMAINS OF ATTRACTIONGLOBAL OPTIMIZATIONLYAPUNOV FUNCTIONNONLINEAR DYNAMIC SYSTEMShttps://purl.org/becyt/ford/2.4https://purl.org/becyt/ford/2In this paper a methodology for the estimation of domains of attraction of stable equilibriums based on maximal Lyapunov functions is proposed. The basic idea consists in finding the best level set of a Lyapunov function which is fully contained in the region of negative definiteness of its time derivative. An optimization problem is formulated, which includes a tangency requirement between the level sets and constraints on the sign of the numerator and denominator of the Lyapunov function. Such constraints help in avoiding a large number of potential dummy solutions of the nonlinear optimization model. Moreover, since global optimality is also required for proper estimation, a deterministic global optimization solver of the branch and bound type is adopted. The methodology is applied to several examples to illustrate different aspects of the approach.Fil: Matallana Perez, Luis Geronimo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Blanco, Anibal Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Bandoni, Jose Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaPergamon-Elsevier Science Ltd2010-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/55939Matallana Perez, Luis Geronimo; Blanco, Anibal Manuel; Bandoni, Jose Alberto; Estimation of domains of attraction: A global optimization approach; Pergamon-Elsevier Science Ltd; Mathematical And Computer Modelling; 52; 3-4; 8-2010; 574-5850895-7177CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.mcm.2010.04.001info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0895717710001913info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-12-03T08:55:14Zoai:ri.conicet.gov.ar:11336/55939instacron: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:34982025-12-03 08:55:14.342CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Estimation of domains of attraction: A global optimization approach
title Estimation of domains of attraction: A global optimization approach
spellingShingle Estimation of domains of attraction: A global optimization approach
Matallana Perez, Luis Geronimo
DOMAINS OF ATTRACTION
GLOBAL OPTIMIZATION
LYAPUNOV FUNCTION
NONLINEAR DYNAMIC SYSTEMS
title_short Estimation of domains of attraction: A global optimization approach
title_full Estimation of domains of attraction: A global optimization approach
title_fullStr Estimation of domains of attraction: A global optimization approach
title_full_unstemmed Estimation of domains of attraction: A global optimization approach
title_sort Estimation of domains of attraction: A global optimization approach
dc.creator.none.fl_str_mv Matallana Perez, Luis Geronimo
Blanco, Anibal Manuel
Bandoni, Jose Alberto
author Matallana Perez, Luis Geronimo
author_facet Matallana Perez, Luis Geronimo
Blanco, Anibal Manuel
Bandoni, Jose Alberto
author_role author
author2 Blanco, Anibal Manuel
Bandoni, Jose Alberto
author2_role author
author
dc.subject.none.fl_str_mv DOMAINS OF ATTRACTION
GLOBAL OPTIMIZATION
LYAPUNOV FUNCTION
NONLINEAR DYNAMIC SYSTEMS
topic DOMAINS OF ATTRACTION
GLOBAL OPTIMIZATION
LYAPUNOV FUNCTION
NONLINEAR DYNAMIC SYSTEMS
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.4
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv In this paper a methodology for the estimation of domains of attraction of stable equilibriums based on maximal Lyapunov functions is proposed. The basic idea consists in finding the best level set of a Lyapunov function which is fully contained in the region of negative definiteness of its time derivative. An optimization problem is formulated, which includes a tangency requirement between the level sets and constraints on the sign of the numerator and denominator of the Lyapunov function. Such constraints help in avoiding a large number of potential dummy solutions of the nonlinear optimization model. Moreover, since global optimality is also required for proper estimation, a deterministic global optimization solver of the branch and bound type is adopted. The methodology is applied to several examples to illustrate different aspects of the approach.
Fil: Matallana Perez, Luis Geronimo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentina
Fil: Blanco, Anibal Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentina
Fil: Bandoni, Jose Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentina
description In this paper a methodology for the estimation of domains of attraction of stable equilibriums based on maximal Lyapunov functions is proposed. The basic idea consists in finding the best level set of a Lyapunov function which is fully contained in the region of negative definiteness of its time derivative. An optimization problem is formulated, which includes a tangency requirement between the level sets and constraints on the sign of the numerator and denominator of the Lyapunov function. Such constraints help in avoiding a large number of potential dummy solutions of the nonlinear optimization model. Moreover, since global optimality is also required for proper estimation, a deterministic global optimization solver of the branch and bound type is adopted. The methodology is applied to several examples to illustrate different aspects of the approach.
publishDate 2010
dc.date.none.fl_str_mv 2010-08
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/11336/55939
Matallana Perez, Luis Geronimo; Blanco, Anibal Manuel; Bandoni, Jose Alberto; Estimation of domains of attraction: A global optimization approach; Pergamon-Elsevier Science Ltd; Mathematical And Computer Modelling; 52; 3-4; 8-2010; 574-585
0895-7177
CONICET Digital
CONICET
url http://hdl.handle.net/11336/55939
identifier_str_mv Matallana Perez, Luis Geronimo; Blanco, Anibal Manuel; Bandoni, Jose Alberto; Estimation of domains of attraction: A global optimization approach; Pergamon-Elsevier Science Ltd; Mathematical And Computer Modelling; 52; 3-4; 8-2010; 574-585
0895-7177
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.mcm.2010.04.001
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0895717710001913
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
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 13.214268

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