  We investigate the optimal control problem for non-Markovian open,
dissipative quantum system. Optimal control using Pontryagin maximum principle
is specifically derived. The influences of Ohmic reservoir with Lorentz-Drude
regularization are numerically studied in a two-level system under the
following three conditions: \omega_0\ll\omega_c, \omega_0\approx\omega_c or
\omega_0\gg\omega_c, where \omega_0 is the characteristic frequency of the
quantum system of interest, and \omega_c the cut-off frequency of Ohmic
reservoir. The optimal control process shows its remarkable influences on the
decoherence dynamics. The temperature is a key factor in the decoherence
dynamics. We analyze the optimal decoherence control in high temperature,
intermediate temperature, and low temperature reservoirs respectively. It
implies that designing some engineered reservoirs with the controlled coupling
and state of the environment can slow down the decoherence rate and delay the
decoherence time. Moreover, we compare the non-Markovian optimal decoherence
control with the Markovian one and find that with non-Markovian the engineered
artificial reservoirs are better than with the Markovian approximation in
controlling the open, dissipative quantum system's decoherence.
