In certain flow regimes, the ideal uniform vehicle flow on the road is unstable, and stop-And-go traffic develops. The instability that leads to this less fuel-efficient unsteady flow results from the collective behavior of all human drivers. This work studies under which circumstances the presence of a single autonomous vehicle (AV) can locally stabilize the flow, without changing the way the humans drive. If possible, this can enable traffic flow control via very few AVs serving as mobile actuators. First, the analysis of car-following models reveals that in idealized conditions (no system noise), the flow can in fact be made linearly stable by means of a low fraction of control vehicles. Second, we highlight the fundamental limitations of this sparse control when considering models with noise.