  In this article we study optimal control problems for systems that are affine
in one part of the control variable. Finitely many equality and inequality
constraints on the initial and final values of the state are considered. We
investigate singular optimal solutions for this class of problems. First, we
obtain second order necessary and sufficient conditions for weak optimality.
Afterwards, we propose a shooting algorithm and show that the sufficient
condition above-mentioned is also sufficient for the local quadratic
convergence of the algorithm.
