  In this work we develop a numerical framework to investigate the
renormalization of the non-Markovian dynamics of an open quantum system to
which dynamical decoupling is applied. We utilize a non-Markovian master
equation which is derived from the non-Markovian quantum trajectories
formalism. It contains incoherent Markovian dynamics and coherent Schr\"odinger
dynamics as its limiting cases and is capable of capture the transition between
them. We have performed comprehensive simulations for the cases in which the
system is either driven by the Ornstein-Uhlenbeck noise or or is described by
the spin-boson model. The renormalized dynamics under bang-bang control and
continuous dynamical decoupling are simulated. Our results indicate that the
renormalization of the non-Markovian dynamics depends crucially on the spectral
density of the environment and the envelop of the decoupling pulses. The
framework developed in this work hence provides an unified approach to
investigate the efficiency of realistic decoupling pulses. This work also opens
a way to further optimize the decoupling via pulse shaping.
