dc.contributor.author Barbero Liñán, María dc.contributor.author Muñoz Lecanda, Miguel Carlos dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV dc.date.accessioned 2008-02-19T17:32:13Z dc.date.available 2008-02-19T17:32:13Z dc.date.issued 2008-02 dc.identifier.citation Muñoz 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.identifier.isbn 0-7354-0546-2 dc.identifier.uri http://hdl.handle.net/2117/1646 dc.description.abstract Pontryagin’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.extent 5 p. dc.language.iso eng dc.publisher American Institute of Physics dc.relation.ispartof International Fall Workshop on Geometry and Physics (XVI : 2007 : Portugal) dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística dc.subject.lcsh Differential equations dc.subject.lcsh Optimization (Mathematics) dc.subject.lcsh Hamiltonian dynamical systems dc.subject.other Pontryagin's Maximum Principle dc.subject.other abnormal extremals dc.subject.other optimal control problems dc.subject.other affine connection control systems dc.title Optimal control problems for affine connection control systems: characterization of extremals dc.type Conference report dc.subject.lemac Equacions diferencials ordinàries dc.subject.lemac Optimització dc.subject.lemac Hamilton, Sistemes de dc.contributor.group Universitat Politècnica de Catalunya. DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions dc.date.end 2007-09-08 dc.date.start 2007-09-05 dc.description.peerreviewed Peer Reviewed dc.subject.ams Classificació AMS::34 Ordinary differential equations::34A General theory dc.subject.ams Classificació AMS::49 Calculus of variations and optimal control; optimization::49K Necessary conditions and sufficient conditions for optimality dc.subject.ams Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics dc.rights.access Open Access
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