Issue |
ESAIM: COCV
Volume 15, Number 1, January-March 2009
|
|
---|---|---|
Page(s) | 173 - 188 | |
DOI | https://doi.org/10.1051/cocv:2008029 | |
Published online | 23 January 2009 |
Smooth optimal synthesis for infinite horizon variational problems
1
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:
30
July
2007
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.