  Based on Lyapunov control, a scheme is proposed to accelerate the dissipation
dynamics for the generation of high-fidelity entanglement between two Rydberg
atoms in the context of cavity quantum electrodynamics (QED). We first use the
quantum Zeno dynamics and Rydberg antiblockade to find a unique steady state
(two-atom singlet state) for the system. Then, applying additional coherent
control (ACC) fields to improve the evolution speed of the dissipative system.
The ACC fields are designed based on the target state and they vanish gradually
along with increasing of the fidelity thus the system is guaranteed to be
finally stable. Besides, the current accelerated scheme is checked to be robust
against systematic and amplitude-noise errors.
