Fundamental Limit on Time Headway for String Stability of Vehicular Platooning

In perhaps the simplest and most economical vehicle platoon control strategy, known as the predecessor-follower topology, time headway is the enabling and in fact the sole means to control inter-vehicle spacing by controlling vehicle speed relative to inter-vehicle distance. While it is desirable to maintain a small time headway to decrease road capacity usage, there is a limit to it in order to ensure the string stability of the platoon and hence secure vehicle safety; string stability, an important concept of platoon scalability, is referred to as the property that disturbances are not amplified when propagating through the platoon. This paper provides an analytical expression of the fundamental lower bound to the time headway allowable to ensure string stability in the predecessor-follower platooning topology. We also analyze the tracking performance of the vehicle system, by presenting an explicit expression of the best achievable tracking error measured under an energy criterion.