  We present a superconvergent Kolmogorov-Arnold-Moser type of perturbation
theory for time-dependent Hamiltonians. It is strictly unitary upon truncation
at an arbitrary order and not restricted to periodic or quasiperiodic
Hamiltonians. Moreover, for pulse-driven systems we construct explicitly the
KAM transformations involved in the iterative procedure. The technique is
illustrated on a two-level model perturbed by a pulsed interaction for which we
obtain convergence all the way from the sudden regime to the opposite adiabatic
regime.
