Fast transitionless expansions of Gaussian anharmonic traps for cold   atoms: bang-singular-bang control
  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. 
Xiao-Jing Lu, Xi Chen, J. Alonso, and J. G. Muga
quant-ph