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Skinner-Rusk Unified Formalism for Optimal Control Systems and Applications

AuthorsBarbero-Liñán, María; Echeverría-Enríquez, Arturo; Martín de Diego, David ; Muñoz-Lecanda, Miguel C.; Roman-Roy, Narciso
KeywordsLagrangian and Hamiltonian formalisms
Jet bundles
Implicit optimal control
Descriptor systems
Issue Date18-Oct-2007
AbstractA 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, providing 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).
DescriptionPublished in: Journal of Physics A: Mathematical and Theoretical, 40 (2007) 12071–12093 (Institute of Physics, ISSN 1751-8121)
Appears in Collections:(ICMAT) Artículos

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