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Unified formalism for higher-order variational problems and its applications in optimal control

Autor
Colombo, L.; P.D. Prieto-Martínez
Tipus d'activitat
Article en revista
Revista
International journal of geometric methods in modern physics
Data de publicació
2014-04-01
Volum
11
Número
4
DOI
https://doi.org/10.1142/S0219887814500340 Obrir en finestra nova
Projecte finançador
Geometría de sistemas físicos y de control y aplicaciones
Red: Geometría, Mecánica y Control
Resum
In this paper, we consider an intrinsic point of view to describe the equations of motion for higher-order variational problems with constraints on higher-order trivial principal bundles. Our techniques are an adaptation of the classical Skinner-Rusk approach for the case of Lagrangian dynamics with higher-order constraints. We study a regular case where it is possible to establish a symplectic framework and, as a consequence, to obtain a unique vector field determining the dynamics. As an inter...
Paraules clau
Constraints, Dynamics, Groupoids, Higher-order systems, Lagrangian and Hamiltonian mechanics, Lagrangian systems, Lie algebroids, Mechanical systems, Reduction, Skinner-Rusk formalism, Submanifolds, constrained variational calculus, optimal control, underactuated mechanical system
Grup de recerca
DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions

Participants

  • Colombo, Leonardo  (autor)
  • Prieto Martinez, Pedro Daniel  (autor)