Stabilizing traffic flow by autonomous vehicles: Stability analysis and implementation considerations.

• Develop a framework including both stability analysis and implementation constraints for traffic platoon control via sparse autonomous vehicles. • Identify the number of human-driven vehicles that can be stabilized by one single autonomous vehicle. • Establish error dynamics in traffic platoon considering multiple disturbances and error composition. • Propose a novel ring string stability that is flexible and applicable to mixed ring traffic. The emergence of autonomous vehicles (AVs) is expected to revolutionize road transportation and it has been demonstrated that AVs can be employed as mobile actuators to effectively dissipate stop and go waves. This paper proposes a comprehensive theoretical framework including stability and implementation considerations for analyzing traffic platoon control via sparse AVs and discussing the number of HDVs that can be stabilized by one AV. Considering multiple disturbance sources, we first discuss the output error composition and analyze traffic dynamics in a platoon system. Then we discuss the Lyapunov asymptotic stability (LAS) of the system based on eigenvalue analysis and propose a novel ring string stability (RSS), which ensures the boundedness of disturbance error and guarantees that the effect of disturbance will not be amplified over a lap. The proposed RSS is flexible and applicable to mixed traffic, since the string instability for predecessor-follower pairs are allowed, provided they can be compensated by AVs. In addition, the practical constraints including driving safety and vehicle physical limitations are modeled. The worst-case evaluation of constraints is conducted to reproduce the critical scenarios in real life. Finally, we conduct numerical experiments and analyze the traffic platoon control from the aspects of both stability and practical implementations. New findings include: (1) The introduction of AVs is beneficial to dampen the waves and stabilize the HDV flow. (2) Considering the implementation issues, there is an upper bound of HDVs that can be stabilized by one single AV. (3) As the number and amplitudes of exogenous disturbances increase, it will be more challenging for sparse AVs to ensure stability and meanwhile satisfy the practical constraints. [ABSTRACT FROM AUTHOR]