  We study the interplay between rotating wave approximation and optimal
control. In particular, we show that for a wide class of optimal control
problems one can choose the control field such that the Hamiltonian becomes
time-independent under the rotating wave approximation. Thus, we show how to
recast the functional minimization defined by the optimal control problem into
a simpler multi-variable function minimization. We provide the analytic
solution to the state-to-state transfer of the paradigmatic two-level system
and to the more general star configuration of an $N$-level system. We
demonstrate numerically the usefulness of this approach in the more general
class of connected acyclic $N$-level systems with random spectra. Finally, we
use it to design a protocol to entangle Rydberg via constant laser pulses atoms
in an experimentally relevant range of parameters.
