We give an effective suffcient 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 on the cotangent bundle T^¤M. The construction uses the curvature of the flow on the cotangent bundle and some ideas of hyperbolic dynamics.

Well-posed infinite horizon variational problems on a compact manifold / Agrachev, Andrey. - In: PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - ISSN 0081-5438. - 268:1(2010), pp. 17-31. [10.1134/S0081543810010037]

Well-posed infinite horizon variational problems on a compact manifold

Agrachev, Andrey
2010-01-01

Abstract

We give an effective suffcient 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 on the cotangent bundle T^¤M. The construction uses the curvature of the flow on the cotangent bundle and some ideas of hyperbolic dynamics.
2010
268
1
17
31
Agrachev, Andrey
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/14035
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