Morse families in optimal control problems
Optimization and Control
2012-11-20 v1 Differential Geometry
Abstract
We geometrically describe optimal control problems in terms of Morse families in the Hamiltonian framework. These geometric structures allow us to recover the classical first order necessary conditions for optimality and the starting point to run an integrability algorithm. Moreover the integrability algorithm is adapted to optimal control problems in such a way that the trajectories originated by discontinuous controls are also obtained. From the Hamiltonian viewpoint we obtain the equations of motion for optimal control problems in the Lagrangian formalism by means of a proper Lagrangian submanifold. Singular optimal control problems and overdetermined ones are also studied along the paper.
Cite
@article{arxiv.1211.4511,
title = {Morse families in optimal control problems},
author = {María Barbero-Liñán and David Iglesias Ponte and David Martín de Diego},
journal= {arXiv preprint arXiv:1211.4511},
year = {2012}
}
Comments
22 pages