Résumé en anglais

The numerical simulation of laser control of molecular systems has made an important step forward by the introduction of algorithms that are guaranteed to improve at each step the cost functional that describes the required control objectives. Nevertheless, after discretization in time, the users may have to deal with instabilities that lead them to stop the simulation indeed with an improved cost functional but before convergence may be reached. In this paper we explain the reasons for such instabilities and propose discrete algorithms that avoid this problem.