  Various constraints concerning control fields can be imposed in the realistic
implementations of quantum control systems. One of the most important is the
restriction on the frequency spectrum of acceptable control parameters. It is
important to consider the limitations of experimental equipment when trying to
find appropriate control parameters. Therefore, in this paper we present a
general method of obtaining a piecewise-constant controls, which are robust
with respect to spectral constraints. We consider here a Heisenberg spin chain,
however the method can be applied to a system with more general interactions.
To model experimental restrictions we apply an ideal low-pass filter to
numerically obtained control pulses. The usage of the proposed method has
negligible impact on the control quality as opposed to the standard approach,
which does not take into account spectral limitations.
