  Combining invariant-based inverse engineering, perturbation theory, and
Optimal Control Theory, we design fast, transitionless expansions of cold
neutral atoms or ions in Gaussian anharmonic traps. Bounding the possible trap
frequencies and using a "bang-singular-bang" control we find fast processes for
a continuum of durations up to a minimum time that corresponds to a purely
bang-bang (stepwise frequency constant) control.
