  We show how second-order Floquet engineering can be employed to realize
systems in which many-body localization coexists with topological properties in
a driven system. This allows one to implement and dynamically control a
topologically-protected qubit even at high energies. Floquet engineering - the
idea that a periodically driven non-equilibrium system can effectively emulate
the physics of a different Hamiltonian - is used to simulate an ffective
three-body interaction among spins in one dimension, using time-dependent
two-body interactions only. In the effective system emulated topology and
disorder coexist which provides an intriguing inroad into the interplay of
many-body localization, defying our standard understanding of thermodynamics,
and topological phases of matter, which are of fundamental and technological
importance. We demonstrate explicitly how combining Floquet engineering,
topology and many-body localization allows one to harvest the advantages
(time-dependent control, topological protection and reduction of heating,
respectively) of each of these sub-fields while protecting from their
disadvantages (heating, static control parameters and strong disorder).
