Probabilistic set invariance and ultimate boundedness

Autores
Kofman, Ernesto Javier; De Doná, José A.; Serón, María Marta
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The notions of invariant sets and ultimate bounds are important concepts in the analysis of dynamical systems and very useful tools for the design of control systems. Several approaches have been reported for the characterisation of these sets, including constructive methods for their computation and procedures to obtain different approximations. However, there are shortcomings in those concepts, in the sense that no general probability distributions can be considered for the disturbances affecting the system (which, for example, precludes the assumption of Gaussian distributions insofar as they are not bounded). Motivated by those shortcomings, we propose in this paper the novel concepts of probabilistic ultimate bounds and probabilistic invariant sets, which extend the notions of invariant sets and ultimate bounds to consider 'containment in probability', and have the important feature of allowing stochastic noises with more general distributions, including the ubiquitous Gaussian distribution, to be considered. We introduce some key definitions for these sets, establish their main properties and develop methods for their computation. A numerical example illustrates the main ideas.
Fil: Kofman, Ernesto Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
Fil: De Doná, José A.. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. University of Newcastle; Reino Unido
Fil: Serón, María Marta. Universidad de Newcastle; Australia
Materia
INVARIANT SETS
LINEAR SYSTEMS
PROBABILISTIC METHODS
ULTIMATE BOUNDS
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:11336/186681
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Probabilistic set invariance and ultimate boundednessKofman, Ernesto JavierDe Doná, José A.Serón, María MartaINVARIANT SETSLINEAR SYSTEMSPROBABILISTIC METHODSULTIMATE BOUNDShttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2The notions of invariant sets and ultimate bounds are important concepts in the analysis of dynamical systems and very useful tools for the design of control systems. Several approaches have been reported for the characterisation of these sets, including constructive methods for their computation and procedures to obtain different approximations. However, there are shortcomings in those concepts, in the sense that no general probability distributions can be considered for the disturbances affecting the system (which, for example, precludes the assumption of Gaussian distributions insofar as they are not bounded). Motivated by those shortcomings, we propose in this paper the novel concepts of probabilistic ultimate bounds and probabilistic invariant sets, which extend the notions of invariant sets and ultimate bounds to consider 'containment in probability', and have the important feature of allowing stochastic noises with more general distributions, including the ubiquitous Gaussian distribution, to be considered. We introduce some key definitions for these sets, establish their main properties and develop methods for their computation. A numerical example illustrates the main ideas.Fil: Kofman, Ernesto Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: De Doná, José A.. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. University of Newcastle; Reino UnidoFil: Serón, María Marta. Universidad de Newcastle; AustraliaPergamon-Elsevier Science Ltd2012-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/186681Kofman, Ernesto Javier; De Doná, José A.; Serón, María Marta; Probabilistic set invariance and ultimate boundedness; Pergamon-Elsevier Science Ltd; Automatica; 48; 10; 10-2012; 2670-26760005-1098CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.automatica.2012.06.074info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0005109812003408info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:23:11Zoai:ri.conicet.gov.ar:11336/186681instacron: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:34982025-09-10 13:23:11.656CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Probabilistic set invariance and ultimate boundedness
title Probabilistic set invariance and ultimate boundedness
spellingShingle Probabilistic set invariance and ultimate boundedness
Kofman, Ernesto Javier
INVARIANT SETS
LINEAR SYSTEMS
PROBABILISTIC METHODS
ULTIMATE BOUNDS
title_short Probabilistic set invariance and ultimate boundedness
title_full Probabilistic set invariance and ultimate boundedness
title_fullStr Probabilistic set invariance and ultimate boundedness
title_full_unstemmed Probabilistic set invariance and ultimate boundedness
title_sort Probabilistic set invariance and ultimate boundedness
dc.creator.none.fl_str_mv Kofman, Ernesto Javier
De Doná, José A.
Serón, María Marta
author Kofman, Ernesto Javier
author_facet Kofman, Ernesto Javier
De Doná, José A.
Serón, María Marta
author_role author
author2 De Doná, José A.
Serón, María Marta
author2_role author
author
dc.subject.none.fl_str_mv INVARIANT SETS
LINEAR SYSTEMS
PROBABILISTIC METHODS
ULTIMATE BOUNDS
topic INVARIANT SETS
LINEAR SYSTEMS
PROBABILISTIC METHODS
ULTIMATE BOUNDS
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv The notions of invariant sets and ultimate bounds are important concepts in the analysis of dynamical systems and very useful tools for the design of control systems. Several approaches have been reported for the characterisation of these sets, including constructive methods for their computation and procedures to obtain different approximations. However, there are shortcomings in those concepts, in the sense that no general probability distributions can be considered for the disturbances affecting the system (which, for example, precludes the assumption of Gaussian distributions insofar as they are not bounded). Motivated by those shortcomings, we propose in this paper the novel concepts of probabilistic ultimate bounds and probabilistic invariant sets, which extend the notions of invariant sets and ultimate bounds to consider 'containment in probability', and have the important feature of allowing stochastic noises with more general distributions, including the ubiquitous Gaussian distribution, to be considered. We introduce some key definitions for these sets, establish their main properties and develop methods for their computation. A numerical example illustrates the main ideas.
Fil: Kofman, Ernesto Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
Fil: De Doná, José A.. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. University of Newcastle; Reino Unido
Fil: Serón, María Marta. Universidad de Newcastle; Australia
description The notions of invariant sets and ultimate bounds are important concepts in the analysis of dynamical systems and very useful tools for the design of control systems. Several approaches have been reported for the characterisation of these sets, including constructive methods for their computation and procedures to obtain different approximations. However, there are shortcomings in those concepts, in the sense that no general probability distributions can be considered for the disturbances affecting the system (which, for example, precludes the assumption of Gaussian distributions insofar as they are not bounded). Motivated by those shortcomings, we propose in this paper the novel concepts of probabilistic ultimate bounds and probabilistic invariant sets, which extend the notions of invariant sets and ultimate bounds to consider 'containment in probability', and have the important feature of allowing stochastic noises with more general distributions, including the ubiquitous Gaussian distribution, to be considered. We introduce some key definitions for these sets, establish their main properties and develop methods for their computation. A numerical example illustrates the main ideas.
publishDate 2012
dc.date.none.fl_str_mv 2012-10
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/11336/186681
Kofman, Ernesto Javier; De Doná, José A.; Serón, María Marta; Probabilistic set invariance and ultimate boundedness; Pergamon-Elsevier Science Ltd; Automatica; 48; 10; 10-2012; 2670-2676
0005-1098
CONICET Digital
CONICET
url http://hdl.handle.net/11336/186681
identifier_str_mv Kofman, Ernesto Javier; De Doná, José A.; Serón, María Marta; Probabilistic set invariance and ultimate boundedness; Pergamon-Elsevier Science Ltd; Automatica; 48; 10; 10-2012; 2670-2676
0005-1098
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.automatica.2012.06.074
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0005109812003408
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/zip
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 12.48226

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