## 1 Introduction  
### Motivations  
Lane change activity is one of the most frequent driving behaviors, significantly impacting traffic efficiency [1, 2]. Compared with the longitudinal-only car-following behavior, the integration of longitudinal and lateral movement complicates the lane change process. The disturbances caused by lane change eventually lead to traffic congestion, resulting in the elongation of travel time and fuel wastage, thus significantly affecting traffic operation [3]. According to statistics presented in [4], lane-changing maneuvers contribute to approximately 4-10% of the total traffic accidents, which correspondingly leads to a 10% delay in the traffic environment. Furthermore, it is noteworthy that 75% of lane change accidents are directly caused by the wrong decision of the drivers [5]. The ongoing development of the connected and automated vehicle (CAV) technology enabled CAVs to perform collaborative driving with each other on the road [6, 7] and showed great potential in addressing the current issues, such as improving safety [8, 9], enhancing mobility [10, 11], improving traffic efficiency [12, 13], and reducing fuel consumption [14, 15], via cooperatively controlling CAVs in traffic environment [16]. Most of these approaches leverage the capabilities of CAV and actively collaborate CAVs in different lane change scenarios to diminish negative effects, such as traffic oscillation or urgent speed change, caused by lane changes [17]. The research works presented in the literature regarding cooperative lane change (CLC) mainly focus on two aspects, i.e., the decision-making strategies before performing a lane change and control strategies in the lane change execution procedure. The decision-making strategies are located on the upper level of a CLC functionality. According to the real-time traffic status of the surrounding environment, these approaches use game theory [18], optimization theory [19; 20], and reinforcement learning [21] methods to evaluate the feasibility of lane change gaps in the target lane and the goal of these methods is usually to mitigate the negative impact of the lane change on the traffic flow in the target lane. The control strategies in a CLC functionality will determine the microscopic control law, such as acceleration/deceleration rate and steering wheel angle, for each controlled CAVs in real-time according to the determined lane change gap from the decision-making strategies. In terms of the controller structure, the control strategies could be classified into two categories, i.e., trajectory planning-tracking and integrated lane change control strategies. The trajectory planning-tracking control strategy is a two-stage controller (i.e., trajectory planning stage and trajectory tracking stage) [22; 23; 24]. The trajectory planning stage generates a reference trajectory with the given lane change gap, which satisfies the requirement of safety, comfort, and traffic efficiency [22]. The trajectory tracking stage determines the microscopic control law and makes each CAV follow the reference trajectory given by the planning stage. In addition, better trajectory tracking control should have dynamic adjustment capabilities such as autonomous collision avoidance when the external road environment changes [25; 26]. Although the planning-tracking control strategy makes the research problems clear and easy to analyze, it usually includes two layers of optimization models, which not only increases the computational burden of the controller but also leads to weak adaptability to dynamic traffic environment in lane change procedure due to the one-time trajectory generation scheme before lane change executing. Compared with the planning-tracking strategy, the integrated lane change controller combines the trajectory and control law generation in an optimization problem with a set of constraints in safety, physical capability, and comfort [27; 28; 29; 30].