In this article we establish for the first time the well-posedness of the shooting algorithm applied to optimal control problems for which all control variables enter linearly in the Hamil- tonian. We start by investigating the case having only initial-final state constraints and free control variable, and afterwards we deal with control bounds. The shooting algorithm is well-posed if the derivative of its associated shooting function is injective at the optimal solution. The main result of this paper is to provide a sufficient condition for this injectivity, that is very close to the second order necessary condition. We prove that this sufficient condition guarantees the stability of the optimal solution under small perturbations and the well-posedness of the shooting algorithm for the perturbed problem. We present numerical tests that validate our method.
INRIA Research Report N° 7763