  Purpose: To employ optimal control for the numerical design of CEST
saturation pulses to maximize contrast and stability against $B_0$
inhomogeneities.
  Theory and Methods: We applied an optimal control framework for the design
pulse shapes for CEST saturation pulse trains. The cost functional minimized
both the pulse energy and the discrepancy between the corresponding CEST
spectrum and the target spectrum based on a continuous RF pulse. The
optimization is subject to hardware limitations. In measurements on a 7 T
preclinical scanner, the optimal control pulses were compared to
continuous-wave and Gaussian saturation methods. We conducted a comparison of
the optimal control pulses were compared to with Gaussian, block pulse trains,
and adiabatic spin-lock pulses.
  Results: The optimal control pulse train demonstrated saturation levels
comparable to continuous-wave saturation and surpassed Gaussian saturation by
up to 50 \% in phantom measurements. In phantom measurements at 3 T the
optimized pulses not only showcased the highest CEST contrast, but also the
highest stability against field inhomogeneities. In contrast, block pulse
saturation resulted in severe artifacts. Dynamic Bloch-McConnell simulations
were employed to identify the source of these artifacts, and underscore the
$B_0$ robustness of the optimized pulses.
  Conclusion: In this work, it was shown that a substantial improvement in
pulsed saturation CEST imaging can be achieved by using Optimal Control design
principles. It is possible to overcome the sensitivity of saturation to B0
inhomogeneities while achieving CEST contrast close to continuous wave
saturation.
