Well-posed infinite horizon variational problems on a compact manifold

Andrei Agrachev

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arXiv · 0906.4433

Well-posed infinite horizon variational problems on a compact manifold

Andrei Agrachev

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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.

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Andrei Agrachev. 2009-10-05. Well-posed infinite horizon variational problems on a compact manifold. https://arxiv.org/abs/0906.4433

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