Ac driven asymmetric pulses can be used to control the Fermi acceleration
between three different motions, A: the {\it accelerated} mode; D: the {\it decelerated} mode and H: the {\it hyperaccelerated} mode.
In this work we show that dissipation strongly affects the particles velocity,
reducing the possibility for an accurate control of the dynamics. The
saturation time, where the mean velocity starts to be constant due to
dissipation, decays with a power law ∼γ−β, where γ is
the dissipation parameter and β is close to 1. The value of the saturated
mean velocity also decays with a power law with exponent β∼0.6 for the
case H, and β∼0.3 for the case A. In the case D this velocity is almost constant for small dissipations.Comment: 5 pages and 4 figs. Accepted in Mathematical Problems in Engineerin