А.А. Аграчев, Корректные вариационные задачи с бесконечным горизонтом на компактном многообразии

Title: Well-posed infinite horizon variational problems
Authors: A.A. Agrachev
Journal title: Proceed. Steklov Math. Inst.
Year: 2010
Volume: 268
Pages: 17-31

A. A. Agrachev, “Well-posed infinite horizon variational problems on a compact manifold”, Proceedings of the Steklov Institute of Mathematics, 2010, 268, 17–31


We give an effective sufficient condition for a variational problem with infinite horizon on a 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.

ArXiv ID (ENG): 0906.4433