Document ESAIM: COCV
DOI: 10.1051/cocv:2008029
Smooth optimal synthesis for infinite horizon variational problems
Andrei A. Agrachev1 and Francesca C. Chittaro21 SISSA, via Beirut 2-4, 34014 Trieste, Italy; agrachev@sissa.it
2 Dipartimento di Matematica Applicata "G. Sansone", via S. Marta 3, 50139 Firenze, Italy; chittaro@math.unifi.it
(Received July 30, 2007. Published online April 26, 2008.)
Abstract
We study Hamiltonian systems which generate extremal flows of regular
variational problems on smooth manifolds and demonstrate that
negativity of the generalized curvature of such a system implies
the existence of a global smooth optimal synthesis for the infinite
horizon problem.
We also show that in the Euclidean case negativity of the generalized curvature is a consequence of
the convexity of the Lagrangian with respect to the pair of arguments. Finally, we give a generic classification for 1-dimensional problems.
Mathematics Subject Classification. 93B50, 49K99
Key words: Infinite-horizon, optimal synthesis, Hamiltonian dynamics
© EDP Sciences, SMAI 2008