Constraint algorithm for extremals in optimal control problems

A characterization of different kinds of extremals of optimal control problems is given if we take an open control set. A well known constraint algorithm for implicit differential equations is adapted to the study of such problems. Some necessary conditions of Pontryagin’s Maximum Principle determin...

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Authors: Barbero Liñán, María, Muñoz Lecanda, Miguel Carlos|||0000-0002-7037-0248
Format: article
Publication Date:2007
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/1167
Online Access:https://hdl.handle.net/2117/1167
Access Level:Open access
Keyword:Differential equations
Optimization (Mathematics)
Lagrangian functions
Hamiltonian dynamical systems
Pontryagin’s Maximum Principle
abnormality
optimal control problems
presymplectic
Equacions diferencials ordinàries
Control òptim, Teoria del
Sistemes dinàmics diferenciables
Lagrange, Funcions de
Classificació AMS::34 Ordinary differential equations::34A General theory
Classificació AMS::49 Calculus of variations and optimal control
optimization::49J Existence theories
optimization::49K Necessary conditions and sufficient conditions for optimality
Classificació AMS::70 Mechanics of particles and systems::70G General models, approaches, and methods
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Àrees temàtiques de la UPC::Matemàtiques i estadística
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oai_identifier_str oai:upcommons.upc.edu:2117/1167
network_acronym_str ES
network_name_str España
repository_id_str
spelling Constraint algorithm for extremals in optimal control problemsBarbero Liñán, MaríaMuñoz Lecanda, Miguel Carlos|||0000-0002-7037-0248Differential equationsOptimization (Mathematics)Lagrangian functionsHamiltonian dynamical systemsPontryagin’s Maximum Principleabnormalityoptimal control problemspresymplecticEquacions diferencials ordinàriesControl òptim, Teoria delSistemes dinàmics diferenciablesLagrange, Funcions deClassificació AMS::34 Ordinary differential equations::34A General theoryClassificació AMS::49 Calculus of variations and optimal controloptimization::49J Existence theoriesClassificació AMS::49 Calculus of variations and optimal controloptimization::49K Necessary conditions and sufficient conditions for optimalityClassificació AMS::70 Mechanics of particles and systems::70G General models, approaches, and methodsClassificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanicsÀrees temàtiques de la UPC::Matemàtiques i estadísticaA characterization of different kinds of extremals of optimal control problems is given if we take an open control set. A well known constraint algorithm for implicit differential equations is adapted to the study of such problems. Some necessary conditions of Pontryagin’s Maximum Principle determine the primary constraint submanifold for the algorithm. Some examples in the control literature, such as subRiemannian geometry and control-affine systems, are revisited to give, in a clear geometric way, a subset where the abnormal, normal and strict abnormal extremals stand.20072007-07-2720072007-08-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/1167reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 2.5 Spainhttp://creativecommons.org/licenses/by-nc-nd/2.5/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/11672026-05-27T15:37:01Z
dc.title.none.fl_str_mv Constraint algorithm for extremals in optimal control problems
title Constraint algorithm for extremals in optimal control problems
spellingShingle Constraint algorithm for extremals in optimal control problems
Barbero Liñán, María
Differential equations
Optimization (Mathematics)
Lagrangian functions
Hamiltonian dynamical systems
Pontryagin’s Maximum Principle
abnormality
optimal control problems
presymplectic
Equacions diferencials ordinàries
Control òptim, Teoria del
Sistemes dinàmics diferenciables
Lagrange, Funcions de
Classificació AMS::34 Ordinary differential equations::34A General theory
Classificació AMS::49 Calculus of variations and optimal control
optimization::49J Existence theories
Classificació AMS::49 Calculus of variations and optimal control
optimization::49K Necessary conditions and sufficient conditions for optimality
Classificació AMS::70 Mechanics of particles and systems::70G General models, approaches, and methods
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short Constraint algorithm for extremals in optimal control problems
title_full Constraint algorithm for extremals in optimal control problems
title_fullStr Constraint algorithm for extremals in optimal control problems
title_full_unstemmed Constraint algorithm for extremals in optimal control problems
title_sort Constraint algorithm for extremals in optimal control problems
dc.creator.none.fl_str_mv Barbero Liñán, María
Muñoz Lecanda, Miguel Carlos|||0000-0002-7037-0248
author Barbero Liñán, María
author_facet Barbero Liñán, María
Muñoz Lecanda, Miguel Carlos|||0000-0002-7037-0248
author_role author
author2 Muñoz Lecanda, Miguel Carlos|||0000-0002-7037-0248
author2_role author
dc.subject.none.fl_str_mv Differential equations
Optimization (Mathematics)
Lagrangian functions
Hamiltonian dynamical systems
Pontryagin’s Maximum Principle
abnormality
optimal control problems
presymplectic
Equacions diferencials ordinàries
Control òptim, Teoria del
Sistemes dinàmics diferenciables
Lagrange, Funcions de
Classificació AMS::34 Ordinary differential equations::34A General theory
Classificació AMS::49 Calculus of variations and optimal control
optimization::49J Existence theories
Classificació AMS::49 Calculus of variations and optimal control
optimization::49K Necessary conditions and sufficient conditions for optimality
Classificació AMS::70 Mechanics of particles and systems::70G General models, approaches, and methods
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Differential equations
Optimization (Mathematics)
Lagrangian functions
Hamiltonian dynamical systems
Pontryagin’s Maximum Principle
abnormality
optimal control problems
presymplectic
Equacions diferencials ordinàries
Control òptim, Teoria del
Sistemes dinàmics diferenciables
Lagrange, Funcions de
Classificació AMS::34 Ordinary differential equations::34A General theory
Classificació AMS::49 Calculus of variations and optimal control
optimization::49J Existence theories
Classificació AMS::49 Calculus of variations and optimal control
optimization::49K Necessary conditions and sufficient conditions for optimality
Classificació AMS::70 Mechanics of particles and systems::70G General models, approaches, and methods
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Àrees temàtiques de la UPC::Matemàtiques i estadística
description A characterization of different kinds of extremals of optimal control problems is given if we take an open control set. A well known constraint algorithm for implicit differential equations is adapted to the study of such problems. Some necessary conditions of Pontryagin’s Maximum Principle determine the primary constraint submanifold for the algorithm. Some examples in the control literature, such as subRiemannian geometry and control-affine systems, are revisited to give, in a clear geometric way, a subset where the abnormal, normal and strict abnormal extremals stand.
publishDate 2007
dc.date.none.fl_str_mv 2007
2007-07-27
2007
2007-08-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/1167
url https://hdl.handle.net/2117/1167
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869415929348096000
score 15,228081

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