Well-posed infinite horizon variational problems on a compact manifold
Optimization and Control
2009-10-05 v3 Dynamical Systems
Abstract
We give an effective sufficient condition for a variational problem with infinite horizon on a compact Riemannian manifold M to admit a smooth optimal synthesis, i. e. a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis we construct a well-projected to M invariant Lagrange submanifold of the extremals' flow in the cotangent bundle T*M. The construction uses the curvature of the flow in the cotangent bundle and some ideas of hyperbolic dynamics.
Cite
@article{arxiv.0906.4433,
title = {Well-posed infinite horizon variational problems on a compact manifold},
author = {Andrei Agrachev},
journal= {arXiv preprint arXiv:0906.4433},
year = {2009}
}