Quantum control addresses the issue of driving a system to a desired objective. Manipulation of quantum systems is achieved by coherent control which relies on constructive and destructive interference of the quantum amplitudes, i.e., quantum coherence. The key ingredient, coherence, is extremely sensitive to any external perturbation. In reality all quantum systems are open, thus, are subject to environmental effects. The interaction with the environment degrades the required agent, coherence, leading to a detrimental effect on coherent control. Quantum control of an open system is therefore a challenge. For this study we employ 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-levels systems, accelerating the approach to equilibrium. Following, we study the generation of quantum non-unitary maps via coherent control. These include both reset maps with complete memory loss. The other extreme where the control is optimized to minimize the dissipation is demonstrated by a single and two qubit unitary maps.
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