  We apply reverse-engineering to find electromagnetic pulses that allow for
the control of populations in quantum systems under dephasing and thermal
noises. In particular, we discuss two-level systems given their importance in
the description of several molecular systems as well as quantum computing. Such
an investigation naturally finds applications in a multitude of physical
situations involving the control of quantum systems. We present an analytical
description of the pulse which solves a constrained dynamics where the initial
and final populations are fixed a priori. This constrained dynamics is
sometimes impossible and we precisely spot the conditions for that. One of our
main results is the presentation of analytical conditions for the establishment
of steady states for finite coherence in the presence of noise. This might
naturally find applications in quantum memories.
