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infinite-horizon

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Smooth optimal synthesis for infinite horizonvariational problems
Andrei A. Agrachev, Francesca C. Chittaro
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 15 / Issue 1 / January 2009

Published online by Cambridge University Press:

23 January 2009, pp. 173-188

Print publication:

January 2009
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We study Hamiltonian systems which generate extremal flows of regularvariational problems on smooth manifolds and demonstrate thatnegativity of the generalized curvature of such a system impliesthe existence of a global smooth optimal synthesis for the infinitehorizon problem.We also show that in the Euclidean case negativity of the generalized curvature is a consequence ofthe convexity of the Lagrangian with respect to the pair of arguments. Finally, we give a generic classification for 1-dimensional problems.