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Smooth optimal synthesis for infinite horizonvariational problems

Published online by Cambridge University Press:  23 January 2009

Andrei A. Agrachev  and
Francesca C. Chittaro
Andrei A. Agrachev
Affiliation:
SISSA, via Beirut 2-4, 34014 Trieste, Italy. agrachev@sissa.it
Francesca C. Chittaro
Affiliation:
Dipartimento di Matematica Applicata “G. Sansone”, via S. Marta 3, 50139 Firenze, Italy. chittaro@math.unifi.it
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Abstract

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.

Keywords

Infinite-horizonoptimal synthesisHamiltonian dynamics
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 1 , January 2009 , pp. 173 - 188
Copyright
© EDP Sciences, SMAI, 2008

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References

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