Bounded stability and eventual string stability of a large platoon of vehicles using non-identical controllers

In this paper the notions of eventual string stability and bounded stability are introduced, and applied to the "constant spacing distance" control problem (in contrast with the "headway control" problem) of a platoon of identical vehicles. In particular, it is assumed that vehicles in the platoon, are controlled by decentralized non-identical controllers, and that it is desired to achieve asymptotic error regulation in the spacing of the vehicles, independent of any constant velocity which the lead vehicle may take, such that the control signals and states of the vehicles in the platoon remain bounded, and such that there exists vehicle N_ by which the system is string stable for all vehicles n > N_ + 1. These properties of a system are called "bounded stability" and "eventual string stability" respectively. A new decentralized controller is proposed which has the property that if the decentralized controller parameters are tuned appropriately, that all the inputs and states of the platoon will remain bounded with respect to the number of vehicles in the platoon, while ensuring asymptotic spacing regulation and eventual string stability of the spacing distance. A number of examples are included which illustrate the type of results which can be obtained for the case of a platoon of size of 1000 vehicles.