  In this work we study how the non-Markovian character of the dynamics can
affect the thermodynamic performance of a quantum thermal engine, by analysing
the maximum power output of Carnot and Otto cycles departing from the
quasi-static and infinite-time-thermalization regime respectively, introducing
techniques for their control optimization in general dynamical models. In our
model, non-Markovianity is introduced by allowing some degrees of freedom of
the reservoirs to be taken into account explicitly and share correlations with
the engine by Hamiltonian coupling. It is found that the non-Markovian effects
can fasten the control and improve the power output.
