The problem of controllability of quantum systems interacting with an engineered environment, whose dynamics are described by a non-Markowian master equation is addressed. The manipulations of the dy- namics is realized with both a laser eld and a tailored non-equilibrium, and generally time-dependent, state of the surrounding environment. Lie algebra theory is used to characterize the structures of the reachable state sets and to prove controllability. The theoretical results are supported by examples.
