Singularities of the hamiltonian vectorfield in
optimal control problems
Abstract
Variational problems with n degrees of freedom give
rise (by Pontriaguine maximum principle) to a hamiltonian
vectorfield in
T*Rn, that
presents singularities (non smoothness points) when the
lagrangean is not convex. For the problems of the calculus of
variations, the singularities that occur are points where the
hamiltonian vectorfield is not C0. For
optimal control problems, we show that besides these
singularities there appear other ones: points where the
hamiltonian vectorfield is C0 but not
C1 and we classify them.