OPTIMAL-CONTROL AND GEODESIC-FLOWS

In this paper we analyze and generalize, from the point of view of the maximum principle, a class of nonlinear optimal control problems orig inally introduced in Brockett (1994). The optimal control problems dis cussed here lie on the adjoint orbits of compact Lie groups or on Gras smann manifolds and the structure of the equations that arise depends on the metric used - the so-called normal metric. We consider some spe cial cases of the general problem and their meaning from the point of view of Riemannian geometry and Hamiltonian mechanics.