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Optimal control problems for affine connection control systems: characterization of extremals
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 |
local.personalitzacitacio | true |