A type of solution to the nonlinear Schrodinger equation for periodically d
riven Bose-Einstein condensates is introduced, which generalizes the famili
ar single-particle Floquet states. These solutions lead to the prediction t
hat the onset of self-trapping of a condensate in a periodically modulated
double well can be systematically controlled. This mean-field prediction is
confirmed on the N-particle level, and explained by a pairing mechanism.