  A sideband cooling strategy that incorporates (i) the dynamics induced by
structured (non-Markovian) environments in the target and auxiliary systems and
(ii) the optimally-time-modulated interaction between them is developed. For
the context of cavity optomechanics, when non-Markovian dynamics are considered
in the target system, ground state cooling is reached at much faster rates and
at much lower phonon occupation number than previously reported. In constrast
to similar current strategies, ground state cooling is reached here for
coupling-strength rates that are experimentally accesible for the
state-of-the-art implementations. After the ultrafast
optimal-ground-state-cooling protocol is accomplished, an additional optimal
control strategy is considered to maintain the phonon number as closer as
possible to the one obtained in the cooling procedure. Contrary to the
conventional expectation, when non-Markovian dynamics are considered in the
auxiliary system, the efficiency of the cooling protocol is undermined.
