  In this manuscript, we investigate optimal control problems which arise in
connection with manipulation of dissipative quantum dynamics. These problems
motivate the study of a class of dissipative bilinear control systems. For
these systems it is shown that the optimal solution and the reachable set can
be found by solving a semidefinite program. In practice, solutions to these
problems generate optimal methods for control of quantum mechanical phenomena
in presence of dissipation. In the area of coherent spectroscopy, this
translates into the maximum signal to noise ratio that can be obtained in a
spectroscopy experiment.
