Geodesic
Smooth optimal synthesis for infinite horizon variational problems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 173-188

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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.

DOI : 10.1051/cocv:2008029
Classification : 93B50, 49K99
Keywords: infinite-horizon, optimal synthesis, hamiltonian dynamics 
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     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://geodesic.mathdoc.fr/articles/10.1051/cocv:2008029/}
}
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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

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