On scalability of platoon of automated vehicles for leader-predecessor information framework

It is well known and broadly accepted that the leader-predecessor framework has been proposed to fix the string instability which is caused by applying the single-predecessor information framework. However, a reasonable but easily neglected fact is that the communication delay between the leading vehicle and the following vehicle is larger than the communication delay between the immediate preceding vehicle and the following vehicle when the large platoon is under consideration. The scalability issue arisen immediately is that whether or not the proposed control laws guaranteeing string stability for the small/medium platoon are suitable for the large platoon. This paper firstly proposes PD control law and sliding model control law for constant distance spacing policy and constant time headway spacing policy respectively, and then proves that both of the two control laws can guarantee string stability for the small/medium platoon. Secondly, it demonstrates that the PD control law for constant distance spacing policy can not guarantee string stability for the large platoon but the sliding model control law for constant time headway spacing policy can. In other words, the sliding model control law for constant time headway spacing policy can make the platoon applying leader-predecessor information framework scalable.