We propose in this paper a gradient-type dynamical system to solve the
problem of maximizing quantum observables for finite dimensional closed quantum
ensembles governed by the controlled Liouville-von Neumann equation. The
asymptotic behavior is analyzed: we show that under the regularity assumption
on the controls the dynamical system almost always converges to a solution of
the maximization problem; we also detail the difficulties related to the
occurrence of singular controls.