  We address edge states and rich localization regimes available in the
one-dimensional (1D) dynamically modulated superlattices, both theoretically
and numerically. In contrast to conventional lattices with straight waveguides,
the quasi-energy band of infinite modulated superlattice is periodic not only
in the transverse Bloch momentum, but it also changes periodically with
increase of the coupling strength between waveguides. Due to collapse of
quasi-energy bands dynamical superlattices admit known dynamical localization
effect. If, however, such a lattice is truncated, periodic longitudinal
modulation leads to appearance of specific edge states that exist within
certain periodically spaced intervals of coupling constants. We discuss unusual
transport properties of such truncated superlattices and illustrate different
excitation regimes and enhanced robustness of edge states in them, that is
associated with topology of the quasi-energy band.
