  Robust time-optimal control is known to feature constant (square) pulses. We
analyze fast adiabatic dynamics that preserve robustness by using alternative
smooth quasi-square pulses, typically represented by hyper-Gaussian pulses. We
here consider the two protocols, robust inverse optimization and
time-contracted adiabatic passage, allowing the design of the same pulse shape
in both cases. The dynamics and their performance are compared. The superiority
of the former protocol is shown.
