Proceedings of the Steklov Institute of Mathematics

, Volume 268, Issue 1, pp 17–31

Well-posed infinite horizon variational problems on a compact manifold


DOI: 10.1134/S0081543810010037

Cite this article as:
Agrachev, A.A. Proc. Steklov Inst. Math. (2010) 268: 17. doi:10.1134/S0081543810010037


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 an invariant Lagrangian submanifold (well-projected to M) of the flow of extremals in the cotangent bundle T*M. The construction uses the curvature of the flow in the cotangent bundle and some ideas of hyperbolic dynamics.

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.SISSA/ISASTriesteItaly
  2. 2.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia