## 1 Introduction  
Traffic bottlenecks are common phenomena in transportation systems and can be categorized into two types: fixed and moving bottlenecks [1]. Fixed bottlenecks occur at specific locations on the road network, such as on-ramps, off-ramps, and toll stations. In contrast, moving bottlenecks can emerge at unpredictable positions along the roadway. Unlike fixed bottlenecks, moving bottlenecks represent more complex traffic phenomena that disrupt the flow of traffic, leading to inefficiencies in both time and space under uncertain conditions. Moving bottlenecks are an inevitable aspect of traffic network operations and can occur at any point on the freeway, often accompanied by uncertainties. These uncertainties may arise from various driving behaviors, including lane changes and acceleration, which result in vehicles clustering at the upstream segment of the bottleneck. Such uncertainty is particularly prevalent in environments characterized by high traffic density and diverse vehicle types. The presence of moving bottlenecks can lead to a significant drop in road capacity over short periods. Moreover, frequent stop-and-go conditions and lane changes in the upstream segment heighten the potential for traffic accidents and can trigger unpredictable emergencies. In the short term, traffic uncertainty negatively impacts transportation infrastructure, leading to increased travel time, air pollution, and fuel consumption [2; 3]. In the long term, it can even affect the lifespan of traffic structures. For instance, [PERSON] et al. [4] argue that traffic events, such as vehicle queuing and other non-uniformly distributed phenomena, can adversely influence the durability of super-long-span bridges. Therefore, researching methods to detect these uncertainties and developing cooperative traffic strategies is essential, offering effective and cost-efficient solutions for enhancing traffic systems [5]. Variable speed limit (VSL) control is a traditional and valid traffic control management method used to mitigate lane-drop bottlenecks [6]. The main idea is to reduce the input ratio of traffic flow in the bottleneck upstream segment by limiting the speed of vehicles in the merging bottleneck upstream area, which will mitigate or alleviate the bottleneck segment congestion by reducing the number of vehicles entering the merging bottleneck area per unit time. The studies on VSL control can be divided into two categories [7]: conventional control strategies and machine learning strategies. The former mainly includes open-loop or closed-loop control strategies based on the traffic flow model; the latter contains deep learning-based methods, reinforcement learning methods, etc. There were some limitations in previous studies. Conventional control strategies are susceptible to system disturbance and the speed limit value cannot adapt to the current traffic state or is heavily dependent on the accuracy of traffic state prediction algorithms. Machine learning strategies need to spend a lot of time training. Additionally, the implementation of previous VSL methods is based on basic road infrastructure, so the scope of control is fixed, not flexible. With the development of vehicular sensing, communications apparatus, technology, and applications, connected automated vehicles (CAVs) have emerged. These vehicles feature close interaction, timely adjustment, and synchronized and coordinated driving, which bring significant safety, mobility, and environmental benefits over non-connected automated vehicles [8]. For example, based on controllability, [PERSON] et al. [9] proposed a three-layered hierarchical control strategy for right-turn merging to improve safety and efficiency. CAVs, equipped with sensor and communication technologies, can sense their surrounding environments and communicate through systems like vehicle-to-infrastructure (V2I) and vehicle-to-vehicle (V2V). This capability provides great potential for addressing lane-drop issues caused by traffic bottlenecks.