Minimum time headway and stabilizing control gains for vehicle platoons with time delay

Abstract

An Adaptive Cruise Control (ACC) system maintains a desired spacing between the vehicles in a platoon through longitudinal control. Maintaining tight longitudinal spacing between vehicles contribute to an increased traffic throughput and road capacity. Most ACC systems adopt a Constant Time Headway Policy (CTHP); a CTHP specifies a desired spacing that is proportional to the speed of the following vehicle with the proportionality constant referred to as the time headway. A smaller time headway leads to enhanced traffic capacity.

Past studies have bounded the minimum time headway which can be stably achieved in the presence of lags. In this study, the minimum limit for time headway achievable with stability guarantees in the presence of bounded time-varying time delays is investigated. Using Hermite-Biehler Theorem for Quasi-Polynomials, the set of all stabilizing control gains of the ACC system is derived as a function of the time headway and the time delay. Similarly, the subset of the above set of control gains preserving string stability is numerically computed.

In this study, it is concluded that for time headway not exceeding twice the upper limit of time delay, there are no control gains that can guarantee individual and string stability. It is observed that for a given time headway, the set of stabilizing control gains during some time delay are stabilizing for any smaller time delay.