  We develop a general approach for monitoring and controlling evolution of
open quantum systems. In contrast to the master equations describing time
evolution of density operators, here, we formulate a dynamical equation for the
evolution of the process matrix acting on a system. This equation is applicable
to non-Markovian and/or strong coupling regimes. We propose two distinct
applications for this dynamical equation. We first demonstrate identification
of quantum Hamiltonians generating dynamics of closed or open systems via
performing process tomography. In particular, we argue how one can efficiently
estimate certain classes of sparse Hamiltonians by performing partial
tomography schemes. In addition, we introduce a novel optimal control theoretic
setting for manipulating quantum dynamics of Hamiltonian systems, specifically
for the task of decoherence suppression.
