Optimal control problems with symmetry breaking cost functions

We investigate symmetry reduction of optimal control problems for left-invariant control affine systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a discrete-time setting as well as the standard continuoustim...

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Detalles Bibliográficos
Autores: Bloch, Anthony M, Colombo, Leonardo, Gupta, Rohit, Ohsawa, Tomoki
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/378446
Acceso en línea:http://hdl.handle.net/10261/378446
Access Level:acceso abierto
Palabra clave:Euler–Poincar´e equations
Lie–Poisson equations
Optimal control
symmetry reduction
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spelling Optimal control problems with symmetry breaking cost functionsBloch, Anthony MColombo, LeonardoGupta, RohitOhsawa, TomokiEuler–Poincar´e equationsLie–Poisson equationsOptimal controlsymmetry reductionWe investigate symmetry reduction of optimal control problems for left-invariant control affine systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a discrete-time setting as well as the standard continuoustime formulation. Specifically, we recast the optimal control problem as a constrained variational problem with a partial symmetry breaking Lagrangian and obtain the Euler–Poincar´e equations from a variational principle. By using a Legendre transformation, we recover the Lie–Poisson equations obtained by Borum and Bretl [IEEE Trans. Automat. Control, 62 (2017), pp. 3209–3224] in the same context. We also discretize the variational principle in time and obtain the discrete-time Lie–Poisson equations. We illustrate the theory with some practical examples including a motion planning problem in the presence of an obstacle.Peer reviewedSociety for Industrial and Applied MathematicsBloch, Anthony M [0000-0003-0235-9765]Colombo, Leonardo [ 0000-0001-6493-6113]Ohsawa, Tomoki [0000-0001-9406-132X]Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202520252017info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10261/378446reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Ingléshttps://doi.org/10.1137/16M1091654Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/3784462026-05-22T06:33:51Z
dc.title.none.fl_str_mv Optimal control problems with symmetry breaking cost functions
title Optimal control problems with symmetry breaking cost functions
spellingShingle Optimal control problems with symmetry breaking cost functions
Bloch, Anthony M
Euler–Poincar´e equations
Lie–Poisson equations
Optimal control
symmetry reduction
title_short Optimal control problems with symmetry breaking cost functions
title_full Optimal control problems with symmetry breaking cost functions
title_fullStr Optimal control problems with symmetry breaking cost functions
title_full_unstemmed Optimal control problems with symmetry breaking cost functions
title_sort Optimal control problems with symmetry breaking cost functions
dc.creator.none.fl_str_mv Bloch, Anthony M
Colombo, Leonardo
Gupta, Rohit
Ohsawa, Tomoki
author Bloch, Anthony M
author_facet Bloch, Anthony M
Colombo, Leonardo
Gupta, Rohit
Ohsawa, Tomoki
author_role author
author2 Colombo, Leonardo
Gupta, Rohit
Ohsawa, Tomoki
author2_role author
author
author
dc.contributor.none.fl_str_mv Bloch, Anthony M [0000-0003-0235-9765]
Colombo, Leonardo [ 0000-0001-6493-6113]
Ohsawa, Tomoki [0000-0001-9406-132X]
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Euler–Poincar´e equations
Lie–Poisson equations
Optimal control
symmetry reduction
topic Euler–Poincar´e equations
Lie–Poisson equations
Optimal control
symmetry reduction
description We investigate symmetry reduction of optimal control problems for left-invariant control affine systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a discrete-time setting as well as the standard continuoustime formulation. Specifically, we recast the optimal control problem as a constrained variational problem with a partial symmetry breaking Lagrangian and obtain the Euler–Poincar´e equations from a variational principle. By using a Legendre transformation, we recover the Lie–Poisson equations obtained by Borum and Bretl [IEEE Trans. Automat. Control, 62 (2017), pp. 3209–3224] in the same context. We also discretize the variational principle in time and obtain the discrete-time Lie–Poisson equations. We illustrate the theory with some practical examples including a motion planning problem in the presence of an obstacle.
publishDate 2017
dc.date.none.fl_str_mv 2017
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Publisher's version
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/378446
url http://hdl.handle.net/10261/378446
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://doi.org/10.1137/16M1091654
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.81155

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