Constructive solution of a bilinear control problem

We present an optimization method of a quantum control problem giving rise to a sequence of controls increasing monotonically the values of a cost functional. We first claim some results about the regularity of this cost functional. Those enable to extend an inequality due to ?ojasiewicz to the infinite dimensional case. Lastly, a sequence of inequalities proving the Cauchy character of the monotonic sequence is obtained, and we can also estimate the rate of convergence. The detailed proof will be given in L. Baudouin, J. Salomon, Constructive solution of a bilinear quantum control problem, 2005, in preparation. 3]]. To cite this article: L. Baudouin, J. Salomon, C. R. Acad. Sci. Paris, Ser. I 342 (2006).