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Smooth optimal synthesis for infinite horizon variational problems

Published online by Cambridge University Press:  23 January 2009

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 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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2008

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References

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Wojtkovski, M.P., Magnetic flows and Gaussian thermostats on manifolds of negative curvature. Fund. Math. 163 (2000) 177191.

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