Motion on lie groups and its applications in control theory

Detalhes bibliográficos
Autor(a) principal: Cariñena, José F.
Data de Publicação: 2003
Outros Autores: Clemente-Gallardo, Jesús, Ramos, Arturo
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/4074
Resumo: The usefulness in control theory of the geometric theory of motion on Lie groups and homogeneous spaces will be shown. We quickly review some recent results concerning two methods to deal with these systems, namely, a generalization of the method proposed by Wei and Norman for linear systems, and a reduction procedure. This last method allows us to reduce the equation on a Lie group G to that on a subgroup H, provided a particular solution of an associated problem in G/H is known. These methods are shown to be very appropriate to deal with control systems on Lie groups and homogeneous spaces, through the specific examples of the planar rigid body with two oscillators and the front-wheel driven kinematic car.
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spelling Motion on lie groups and its applications in control theoryDrift-free control systemsWei-Norman methodmotion in Lie groups and homogeneous spacesreductionThe usefulness in control theory of the geometric theory of motion on Lie groups and homogeneous spaces will be shown. We quickly review some recent results concerning two methods to deal with these systems, namely, a generalization of the method proposed by Wei and Norman for linear systems, and a reduction procedure. This last method allows us to reduce the equation on a Lie group G to that on a subgroup H, provided a particular solution of an associated problem in G/H is known. These methods are shown to be very appropriate to deal with control systems on Lie groups and homogeneous spaces, through the specific examples of the planar rigid body with two oscillators and the front-wheel driven kinematic car.http://www.sciencedirect.com/science/article/B6VN0-49F836Y-3/1/3e135eb33cca05a026b85455b55443082003info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleaplication/PDFhttp://hdl.handle.net/10316/4074http://hdl.handle.net/10316/4074engReports on Mathematical Physics. 51:2-3 (2003) 159-170Cariñena, José F.Clemente-Gallardo, JesúsRamos, Arturoinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2020-05-25T12:06:01Zoai:estudogeral.uc.pt:10316/4074Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:57:53.108360Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Motion on lie groups and its applications in control theory
title Motion on lie groups and its applications in control theory
spellingShingle Motion on lie groups and its applications in control theory
Cariñena, José F.
Drift-free control systems
Wei-Norman method
motion in Lie groups and homogeneous spaces
reduction
title_short Motion on lie groups and its applications in control theory
title_full Motion on lie groups and its applications in control theory
title_fullStr Motion on lie groups and its applications in control theory
title_full_unstemmed Motion on lie groups and its applications in control theory
title_sort Motion on lie groups and its applications in control theory
author Cariñena, José F.
author_facet Cariñena, José F.
Clemente-Gallardo, Jesús
Ramos, Arturo
author_role author
author2 Clemente-Gallardo, Jesús
Ramos, Arturo
author2_role author
author
dc.contributor.author.fl_str_mv Cariñena, José F.
Clemente-Gallardo, Jesús
Ramos, Arturo
dc.subject.por.fl_str_mv Drift-free control systems
Wei-Norman method
motion in Lie groups and homogeneous spaces
reduction
topic Drift-free control systems
Wei-Norman method
motion in Lie groups and homogeneous spaces
reduction
description The usefulness in control theory of the geometric theory of motion on Lie groups and homogeneous spaces will be shown. We quickly review some recent results concerning two methods to deal with these systems, namely, a generalization of the method proposed by Wei and Norman for linear systems, and a reduction procedure. This last method allows us to reduce the equation on a Lie group G to that on a subgroup H, provided a particular solution of an associated problem in G/H is known. These methods are shown to be very appropriate to deal with control systems on Lie groups and homogeneous spaces, through the specific examples of the planar rigid body with two oscillators and the front-wheel driven kinematic car.
publishDate 2003
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dc.relation.none.fl_str_mv Reports on Mathematical Physics. 51:2-3 (2003) 159-170
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