Smooth optimal synthesis for infinite horizon variational problems
Andrei A. Agrachev; Francesca C. Chittaro
ESAIM: Control, Optimisation and Calculus of Variations (2009)
- Volume: 15, Issue: 1, page 173-188
- ISSN: 1292-8119
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topAgrachev, Andrei A., and Chittaro, Francesca C.. "Smooth optimal synthesis for infinite horizon variational problems." ESAIM: Control, Optimisation and Calculus of Variations 15.1 (2009): 173-188. <http://eudml.org/doc/250545>.
@article{Agrachev2009,
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.
},
author = {Agrachev, Andrei A., Chittaro, Francesca C.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Infinite-horizon; optimal synthesis; Hamiltonian dynamics; infinite-horizon},
language = {eng},
month = {1},
number = {1},
pages = {173-188},
publisher = {EDP Sciences},
title = {Smooth optimal synthesis for infinite horizon variational problems},
url = {http://eudml.org/doc/250545},
volume = {15},
year = {2009},
}
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
DA - 2009/1//
PB - EDP Sciences
VL - 15
IS - 1
SP - 173
EP - 188
AB -
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.
LA - eng
KW - Infinite-horizon; optimal synthesis; Hamiltonian dynamics; infinite-horizon
UR - http://eudml.org/doc/250545
ER -
References
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- R.V. Gamkrelidze, Principles of Optimal Control Theory. Plenum Press, New York (1978).
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- A.V. Sarychev and D.F.M. Torres, Lipschitzian regularity of minimizers for optimal control problems with control-affine dynamics. Appl. Math. Optim.41 (2000) 237–254.
- M.P. Wojtkovski, Magnetic flows and Gaussian thermostats on manifolds of negative curvature. Fund. Math.163 (2000) 177–191.
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