  We introduce the notion of adiabatic state-flip of a Floquet Hamiltonian
associated with a non-Hermitian system that it is subjected to two driving
schemes with clear separation of time scales. The fast (Floquet) modulation
scheme is utilized to re-allocate the exceptional points in the parameter space
of the system and re-define the topological features of an adiabatic cyclic
modulation associated with the slow driving scheme. Such topological
re-organization can be used in order to control the adiabatic transport between
two eigenmodes of the Floquet Hamiltonian. The proposed scheme provides a
degree of reconfigurability of adiabatic state transfer which can find
applications in system control in photonics and microwave domains.
