| Abstract: |
| In this talk we discuss a geometric approach to certain optimal
control problems and we discuss their relationship to some classical integrable
Hamiltonian systems and their generalizations. We consider
kinematic optimal control problems on manifolds
corresponding to the infinitesimal generator of a group action.
The integrable systems discussed include
the rigid body equations, geodesic flows on the ellipsoid, flows
on Stiefel manifolds, and the Toda lattice
flows. We discuss the Hamiltonian structure of these systems, relate
our work to some work of Moser and discuss some generalizations. This
is mainly joint work with Francois Gay Balmaz and Tudor Ratiu. |
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