Equalization of intervehicular distances in platoons on a circular track

We consider a circular track and a platoon of vehicles driving on it. Our goal is to design a distributed (onboard) control system that will keep uniform spacing between any car and its predecessor without knowing the length of the track. Quite naturally the distributed control problem is posed as a double consensus task, wherein individual cars have to agree on the cruising velocity and the gaps between two consecutive cars. We study the feasibility of the consensus and its convergence properties. We prove that the cars will converge to equal distances and the resulting velocity will be the average of the velocity references of individual cars. We also consider the stability of this circularly connected system.