Disturbance Propagation in Vehicle Platoons: Symmetric Bidirectional Interconnections

This paper is concerned with the problem of disturbance propagation in interconnected systems with double-integrator open-loop dynamics (e.g. acceleration-controlled automated vehicles). We consider a symmetric bidirectional linear interconnection to control the vehicles, in which each vehicle is interconnected solely to one immediate predecessor and to one immediate follower with the same control gain in these two directions. We prove that in this setting, regardless of the choice of stabilizing controller, it is not possible to keep the displacements between the vehicles bounded, and they grow unbounded depending on the number of vehicles N. In this case, we call the system string unstable. We show that this impossibility of achieving string stability remains under various boundary conditions for the leading vehicle, i.e., whether this is a virtual or physical vehicle.