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dc.contributor.authorBarbero Liñán, María
dc.contributor.authorMuñoz Lecanda, Miguel Carlos
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.identifier.citationMuñoz Lecanda, Miguel Carlos. “ Optimal control problems for affine connection control systems: characterization of extremals”. A: AIP Conference Proceedings. Geometry and physics: XVI International Fall Workshop. 2008, vol. 1023, p. 127-131. ISBN 978-0-7354-0546-2
dc.description.abstractPontryagin’s Maximum Principle [8] is considered as an outstanding achievement of optimal control theory. This Principle does not give sufficient conditions to compute an optimal trajectory; it only provides necessary conditions. Thus only candidates to be optimal trajectories, called extremals, are found. Maximum Principle gives rise to different kinds of them and, particularly, the so-called abnormal extremals have been studied because they can be optimal, as Liu and Sussmann, and Montgomery proved in subRiemannian geometry [5, 7]. We build up a presymplectic algorithm, similar to those defined in [2, 3, 4, 6], to determine where the different kinds of extremals of an optimal control problem can be. After describing such an algorithm, we apply it to the study of extremals, specially the abnormal ones, in optimal control problems for affine connection control systems [1]. These systems model the motion of different types of mechanical systems such as rigid bodies, nonholonomic systems and robotic arms [1].
dc.format.extent5 p.
dc.publisherAmerican Institute of Physics
dc.relation.ispartofInternational Fall Workshop on Geometry and Physics (XVI : 2007 : Portugal)
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshDifferential equations
dc.subject.lcshOptimization (Mathematics)
dc.subject.lcshHamiltonian dynamical systems
dc.subject.otherPontryagin's Maximum Principle
dc.subject.otherabnormal extremals
dc.subject.otheroptimal control problems
dc.subject.otheraffine connection control systems
dc.titleOptimal control problems for affine connection control systems: characterization of extremals
dc.typeConference report
dc.subject.lemacEquacions diferencials ordinàries
dc.subject.lemacHamilton, Sistemes de
dc.contributor.groupUniversitat Politècnica de Catalunya. DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::34 Ordinary differential equations::34A General theory
dc.subject.amsClassificació AMS::49 Calculus of variations and optimal control; optimization::49K Necessary conditions and sufficient conditions for optimality
dc.subject.amsClassificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
dc.rights.accessOpen Access

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