  We develop a Markovian master equation that models the evolution of systems
subject to arbitrary driving and control fields. Our approach combines time
rescaling and weak-coupling limits for the system-environment interaction with
a secular approximation. The derivation makes use of the adiabatic time
evolution operator in a manner that allows for the efficient description of
strong driving, while recovering the adiabatic master equation in the
appropriate limit. To illustrate the effectiveness of our approach, we apply it
to the paradigmatic case of a two-level (qubit) system subjected to a form of
periodic driving that remains unsolvable using a Floquet representation. We
demonstrate the reliability and broad scope of our approach by benchmarking the
solutions of the derived reduced time evolution against numerically exact
simulations using tensor networks. Our results provide rigorous conditions that
must be satisfied by phenomenological master equations for driven systems that
do not rely on first principles derivations.
