descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 18 Sep 2007Embargo end date: 01 Jan 2007Publisher:IOP PublishingJournal:Journal of Physics A: Mathematical and Theoretical, volume 40, pages 12,071-12,093 (issn: 1751-8113, eissn: 1751-8121,

Authors: Barbero Liñán, María; Echeverría Enríquez, Arturo; Martín de Diego, David; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso;

doi: 10.1088/1751-8113/40/40/005 , 10.48550/arxiv.0705.2178

arXiv: http://arxiv.org/abs/0705.2178

handle: 2117/1013

Skinner–Rusk unified formalism for optimal control systems and applications

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Abstract

A geometric approach to time-dependent optimal control problems is proposed. This formulation is based on the Skinner and Rusk formalism for Lagrangian and Hamiltonian systems. The corresponding unified formalism developed for optimal control systems allows us to formulate geometrically the necessary conditions given by Pontryagin's Maximum Principle, provided that the differentiability with respect to controls is assumed and the space of controls is open. Furthermore, our method is also valid for implicit optimal control systems and, in particular, for the so-called descriptor systems (optimal control problems including both differential and algebraic equations).

26 pp. Replaced with the published version. Section 2 has been shortened. Minor mistakes are corrected

Related Organizations

Universitat Politècnica de Catalunya
Spain
Spanish National Research Council
Spain
Universitat Polite`cnica de Catalunya
Spain
Instituto de Física Fundamental
Spain

Keywords

70G45, 49J15, 34A26, 49K15, 70H03, 70H05, and methods, implicit optimal control systems, FOS: Physical sciences, Lagrangian and Hamiltonian formalisms, Control òptim, Teoria del, Teoria del, jet bundles, Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics, :34 Ordinary differential equations::34A General theory [Classificació AMS], :70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics [Classificació AMS], Hamilton, Jet bundles, Hamiltonian systems, descriptor systems, :49K Necessary conditions and sufficient conditions for optimality [optimization], Mathematical Physics, :70 Mechanics of particles and systems::70G General models, approaches, and methods [Classificació AMS], Equacions de, approaches, Lagrange equations, Lagrange, Classificació AMS::49 Calculus of variations and optimal control; optimization::49K Necessary conditions and sufficient conditions for optimality, Mathematical Physics (math-ph), Classificació AMS::70 Mechanics of particles and systems::70G General models, Classificació AMS::70 Mechanics of particles and systems::70G General models, approaches, and methods, :49J Existence theories [optimization], Implicit optimal control, optimization::49K Necessary conditions and sufficient conditions for optimality, Sistemes de, :49 Calculus of variations and optimal control [Classificació AMS], Lagrange, Equacions de, Control òptim, Hamilton, Sistemes de, Classificació AMS::49 Calculus of variations and optimal control, optimization::49J Existence theories, Classificació AMS::34 Ordinary differential equations::34A General theory, Classificació AMS::49 Calculus of variations and optimal control; optimization::49J Existence theories, Descriptor systems

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