Optimal control on adjoint orbits and symmetric spaces

In this paper we analyze and generalize, from the point of view of the maximum principle, a class of nonlinear optimal control problems originally introduced in Brockett (1994). The optimal control problems that we consider here lie on the adjoint orbits of compact Lie groups or on Grassmann manifolds. An important role is played by the type of metric used-the so called normal metric. We consider some special cases of the general problem and their meaning from the point of view of Riemannian geometry and Hamiltonian mechanics