This work is dedicated to the analysis of the delicate details of the effect of upstream velocity fluctuations on the flame propagation speed. The investigation was carried out using the Sivashinsky model of cellularization of hydrodynamically unstable flame fronts. We identified the perturbations of the steadily propagating flames which can be significantly amplified over finite periods of time. These perturbations were used to model the effect of upstream velocity fluctuations on the flame front dynamics and to study a possibility to control the flame propagation speed.