The subject of this talk was the development of the Maximum Principle for
affine connection control systems. You will recall that the control
equations for a general control system, coupled with the so-called adjoint
equations, define a time-dependent Hamiltonian system, and that all optimal
trajectories are projections of integral curves of this Hamiltonian system.
The adjoint equation describing the evolution of the Lagrange multipliers
along the optimal trajectory is not generally by itself an intrinsic object.
However, we show that for affine connection control systems one *can*
extract the adjoint equation in an intrinsic way, and that the resulting
equation, which we call the *adjoint Jacobi equation*, is related to
the Jacobi equation which describes the variation of geodesics.

No online version avaliable (but check this out).