Well-posed infinite horizon variational problems on a compact manifold

Details Well-posed infinite horizon variational problems on a compact manifold Well-posed infinite horizon variational problems on a compact manifold

2009-06-24

arxiv.org/abs/0906.4433v3

Mathematics

Optimization and Control

Scientific paper

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.

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