  Floquet engineering offers tantalizing opportunities for controlling the
dynamics of quantum many body systems and realizing new nonequilibrium phases
of matter. However, this approach faces a major challenge: generic interacting
Floquet systems absorb energy from the drive, leading to uncontrolled heating
which washes away the sought after behavior. How to achieve and control a
non-trivial nonequilibrium steady state is therefore of crucial importance. In
this work, we study the dynamics of an interacting one-dimensional
periodically-driven electronic system coupled to a phonon heat bath. Using the
Floquet-Boltzmann equation (FBE) we show that the electronic populations of the
Floquet eigenstates can be controlled by the dissipation. We find the regime in
which the steady state features an insulatorlike filling of the Floquet bands,
with a low density of additional excitations. Furthermore, we develop a simple
rate equation model for the steady state excitation density that captures the
behavior obtained from the numerical solution of the FBE over a wide range of
parameters.
