A characterization of different kinds of extremals of optimal control problems
is given if we take an open control set. A well known constraint algorithm for
implicit differential equations is adapted to the study of such problems. Some
necessary conditions of Pontryagin’s Maximum Principle determine the primary
constraint submanifold for the algorithm. Some examples in the control literature,
such as subRiemannian geometry and control-affine systems, are revisited
to give, in a clear geometric way, a subset where the abnormal, normal and strict
abnormal extremals stand.