Motion on lie groups and its applications in control theory
Autor(a) principal: | |
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Data de Publicação: | 2003 |
Outros Autores: | , |
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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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 |
dc.date.none.fl_str_mv |
2003 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10316/4074 http://hdl.handle.net/10316/4074 |
url |
http://hdl.handle.net/10316/4074 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Reports on Mathematical Physics. 51:2-3 (2003) 159-170 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
aplication/PDF |
dc.source.none.fl_str_mv |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799133868179062784 |