  We study the persistence of localization for a strongly disordered
tight-binding Anderson model on the lattice $\mathbb{Z}^d$, periodically driven
on each site. Under two different sets of conditions, we show that Anderson
localization survives if the driving frequency is higher than some threshold
value that we determine. We discuss the implication of our results for recent
development in condensed matter physics, we compare them with the predictions
issuing from adiabatic theory, and we comment on the connexion with Mott's law,
derived within the linear response formalism.
