  Quantum control of an open system is demonstrated employing a
thermodynamically consistent master equation. In this framework, the open
system dynamics depend on the control protocol due to the dressing of the
system by the drive. This interrelation serves as the key element for control.
The influence of the external drive is incorporated within the dynamical
equation, enabling an indirect control of the dissipation. The control paradigm
is displayed by analyzing entropy changing state to state transformations,
heating and cooling N-level systems. Following, we study the generation of
quantum non-unitary maps via coherent control. These include both reset maps
with complete memory loss and single-qubit unitary maps under dissipative
conditions.
