  We propose a fast mixed-state control scheme to transfer the quantum state
along designable trajectories in Hilbert space, which is robust to multiple
decoherence noises. Starting with the dynamical invariants of open quantum
systems, we present the shortcuts to adiabaticity (STAs) of open quantum
systems at first, then apply the STAs to speed up the adiabatic steady process.
Our scheme drives open systems from a initial steady state to a target steady
state by a controlled Liouvillian that possesses the same form as the reference
(original) one which is accessible in present-day experiments. The experimental
observation with current available parameters for the nitrogen-vacancy (NV)
center in diamond is suggested and discussed.
