I. Introduction
The development of Connected and Automated Vehicle (CAV) technology provides a new mode for vehicle driving, namely the platoon-based driving mode. Platooning has attracted much attention due to its advantages of improving traffic efficiency, reducing accident rates, and alleviating traffic congestion [1], [2], [3]. The structure of the platoon is not fixed in the driving process. Flexible platoon expansion needs to respond to the dynamic merging requirements of vehicles. Therefore, in the design of the platoon system, it is an important goal to control vehicles to merge into the platoon efficiently, safely, and stably [4]. The vehicle merging process requires dynamic adjustment between the platoon vehicles and the merging vehicles, and at the same time, the safety and stability of the platoon should be ensured, which puts forward strict requirements for the longitudinal control of vehicles merging into a platoon [5]. When multiple vehicles merge into the same platoon, the problem becomes more complicated.