  We characterize the impact that the application of two maps in a
quantum-controlled order has on the process of work extraction via unitary
cycles and its optimization. The control is based on the quantum switch model
that applies maps in an order not necessarily compatible with the underlying
causal structure and, in principle, can be implemented experimentally. First,
we show that the activation of quantum maps through the quantum switch model
always entails a non-negative gain in ergotropy compared to their consecutive
application. We also establish a condition that the maps should fulfill in
order to achieve a non-zero ergotropic gain. We then perform a thorough
analysis of maps applied to a two-level system and provide general conditions
for achieving a positive gain on the incoherent part of ergotropy. Our results
are illustrated with several examples and applied to qubit and $d$-dimensional
quantum systems. In particular, we demonstrate that a non-zero work can be
extracted from a system thermalized by two coherently controlled reservoirs.
