This paper deals with optimal control problems for systems that are affine in one part of the control variables and nonlinear in the rest of the control variables. We have finitely many equality and inequality constraints on the initial and final states. First we obtain second order necessary and sufficient conditions for weak optimality. Afterwards, we propose a shooting algorithm, and we show that the sufficient condition above-mentioned is also sufficient for the injectivity of the shooting function at the solution.
INRIA Research Report Nr. 7764