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.
Smooth Optimal Synthesis for infinite horizon variational problems / Agrachev, A. A.; Chittaro, F. C.. - In: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. - ISSN 1262-3377. - 15:1(2009), pp. 173-188. [10.1051/cocv:2008029]
Smooth Optimal Synthesis for infinite horizon variational problems
CHITTARO F. C.
2009-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
