## 2 Problem Statement  
This work proposes a novel CLC control strategy in a pure CAV traffic flow by considering a two-lane highway, as presented in Figure 1. Specifically, we mainly focus on the movements of four vehicles, including the host CAV intending to change lanes (vehicle M) and three surrounding vehicles (vehicles A, B, and C). As presented, vehicles A and B denote the following and preceding vehicles of vehicle M in the target lane, respectively. Vehicle C is the preceding vehicle of vehicle M in the original lane. The longitudinal position, speed, and acceleration of vehicle \(i\) (where \(i=\{\text{M},\text{ A},\text{ B},\text{ C}\}\)) are denoted as \(x_{i}\), \(v_{i}\), and \(a_{i}\), respectively. Vehicle M obtains the aforementioned motion state information in real-time based on onboard sensors and V2V communication. Vehicle M leaves the original lane behind vehicle C and enters the target lane when the gap constraint between vehicles A and B is satisfied. Since vehicles B and C are driving with free flow states forming a stable car-following state with their preceding vehicles, there may not be enough space for coordinated control. Therefore, if vehicle M sends a CLC request in its ambient area, vehicle A can act as the cooperative vehicle employing V2V communication to form a cooperative relationship with vehicle M. Based on the aforementioned lane-changing scenario, vehicle A provides suitable space for vehicle M for changing lanes by adjusting its speed to improve the success rate of lane change of vehicle M. Additionally, the vehicle M ensures a safe gap from vehicle C by adjusting its speed. When vehicle M is about to leave the original lane and enter the target lane, vehicles A and M should update their tracked preceding vehicles, i.e., switching from vehicles M and C to vehicles M and B, respectively, and reach their expected motion state without disturbing the traffic flow. Based on the previous description, we divide the whole lane-changing process into two stages, including the lane change process in the original lane (LC-O) stage and the lane change process in the target lane (LC-T) stage, as presented in Figure 2. The LC-T stage follows the LC-O stage and includes its subsequent car-following phase after the lane change vehicle enters the target lane. During the lane-changing process, vehicle M performs both lateral and longitudinal movements. At the same time, vehicle A adjusts its longitudinal motion based on the CLC control strategy. In this work, the longitudinal accelerations of vehicles M and A are coordinately determined by the proposed optimization model. The proposed model considers the disturbance produced by a lane change maneuver and its negative effect on an ambient area. On the other hand, the lateral acceleration changes according to an appropriate lateral motion trajectory model. During the LC-O stage, vehicle M collaborates with vehicle A to ensure that the vehicle M enters in the target lane safely and effectively on the premise of less impact on the traffic flow of the target lane. In the LC-T stage, vehicle M gradually enters in the target lane and drives in cooperation with vehicle A to achieve the desired car-following states among vehicles M, A, and B. In order to further support the proposed approach, we make the following assumptions:  
1. All the CAVs involved in this work can share real-time information accurately and timely based on V2V communication [38]. It is assumed that there is no packet loss and communication delay during the process of information sharing. 2. The CAVs are equipped with high-precision onboard sensors, which can accurately measure the position, speed, and acceleration of the vehicles. 3. This work adopts a lateral and longitudinal separation structure [39; 30]. 4. Vehicles M and A follow the same upper and lower bounds of acceleration constraints. Figure 1: The CLC scenario on a two-lane highway. Figure 2: The two stages of the lane change.