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.
Mots-clés : infinite-horizon, optimal synthesis, hamiltonian dynamics
@article{COCV_2009__15_1_173_0,
author = {Agrachev, Andrei A. and Chittaro, Francesca C.},
title = {Smooth optimal synthesis for infinite horizon variational problems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {173--188},
publisher = {EDP-Sciences},
volume = {15},
number = {1},
year = {2009},
doi = {10.1051/cocv:2008029},
mrnumber = {2488574},
zbl = {1158.49039},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv:2008029/}
}
TY - JOUR AU - Agrachev, Andrei A. AU - Chittaro, Francesca C. TI - Smooth optimal synthesis for infinite horizon variational problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2009 SP - 173 EP - 188 VL - 15 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2008029/ DO - 10.1051/cocv:2008029 LA - en ID - COCV_2009__15_1_173_0 ER -
%0 Journal Article %A Agrachev, Andrei A. %A Chittaro, Francesca C. %T Smooth optimal synthesis for infinite horizon variational problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2009 %P 173-188 %V 15 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2008029/ %R 10.1051/cocv:2008029 %G en %F COCV_2009__15_1_173_0
Agrachev, Andrei A.; Chittaro, Francesca C. Smooth optimal synthesis for infinite horizon variational problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 173-188. doi : 10.1051/cocv:2008029. http://archive.numdam.org/articles/10.1051/cocv:2008029/
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