  Manipulation of a quantum system requires the knowledge of how it evolves. To
impose that the dynamics of a system becomes a particular target operation (for
any preparation of the system), it may be more useful to have an equation of
motion for the dynamics itself--rather than the state. Here we develop a
Markovian master equation for the process matrix of an open system, which
resembles the Lindblad Markovian master equation. We employ this equation to
introduce a scheme for optimal local coherent process control at target times,
and extend the Krotov technique to obtain optimal control. We illustrate
utility of this framework through several quantum coherent control scenarios,
such as optimal decoherence suppression, gate simulation, and passive control
of the environment, in all of which we aim to simulate a given terminal process
at a given final time.
