  We study coherent quantum control strategy which is robust with respect to
coupling with an external environment. We model this interaction by appending
an additional subsystem to the initial system and we choose the strength of the
coupling to be proportional to the magnitude of the control pulses. Therefore,
to minimize the interaction we impose $L_1$ norm restrictions on the control
pulses. In order to efficiently solve this optimization problem we employ the
BFGS algorithm. We use three different functions as the derivative of the $L1$
norm of control pulses: the signum function, a fractional derivative
$\frac{\dd^\alpha |x|}{\dd x^\alpha}$, where $0<\alpha<1$, and the Fermi-Dirac
distribution. We show that our method allows to efficiently obtain the control
pulses which neglect the coupling with an external environment.
