  We consider a nonlinear system, affine with respect to an unbounded control
$u$ which is allowed to range in a closed cone. To this system we associate a
Bolza type minimum problem, with a Lagrangian having sublinear growth with
respect to $u$. This lack of coercivity gives the problem an {\it impulsive}
character, meaning that minimizing sequences of trajectories happen to converge
towards discontinuous paths. As is known, a distributional approach does not
make sense in such a nonlinear setting, where, instead, a suitable embedding in
the graph-space is needed.
  We provide higher order necessary optimality conditions for properly defined
impulsive minima, in the form of equalities and inequalities involving iterated
Lie brackets of the dynamical vector fields. These conditions are derived under
very weak regularity assumptions and without any constant rank conditions.
