## 2 Related Work  
In this section, we introduce the detailed classification of conventional methods and machine learning methods for VSL control, respectively. The conventional method for VSLs includes open-loop control, closed-loop control method, and model-based control method. In terms of an open-loop control, this method is relatively simple and used in VSLs control strategy without feedback adjustment according to the corresponding effect. Early studies mostly used this kind of control algorithm. Still, open-loop control is susceptible to system disturbance and cannot obtain a speed limit value adapted to the current traffic state. For example, [PERSON] et al. [10] proposed a speed control method termed variable speed release to increase bottleneck capacity. Closed-loop control (feedback control) has a feedback path connecting the input and output inside the control system. The outcome of the control system is transmitted to the input end together with the input signal as the input of the next stage, which can alleviate the system's uncertain factors and disturbances to improve the system's accuracy and stability. Compared with the open-loop control system, the algorithm of the closed-loop control system is fast in the calculation, the structure is simple, and the stability is high. It can be used in large-scale practical applications. [PERSON] et al. [11] developed a novel bang-bang feedback control speed harmonization (SH) or VSL method, which attempts to prevent or delay the breakdown of a bottleneck and thus reduce traffic congestion. [PERSON] et al. [12] focused on the backstepping state feedback control to stabilize a moving shockwave in a freeway segment under bilateral boundary actuation of traffic flow. [PERSON] et al. [13] proposed an interacting multi-modeling approach with a pseudo-modeling set (IMMP) to achieve VSL control with fault tolerance to various types of recurrent sensor faults (RSFs). [PERSON] et al. [14; 15] proposed a logic-based traffic flow control (LB-TFC) algorithm for the integrated control of ramp metering (RM) installations and variable speed limits (VSLs) to reduce traffic jams at bottlenecks. [PERSON] et al. [16] presented a dynamic freeway speed controller based on the sliding mode theory, which uses the fundamental equations governing traffic dynamics in combination with variable speed limit control to provide advisory speeds for connected vehicles. Model-based control is more popular to solve traffic problems. Moreover, the model predictive control (MPC) framework has shown great potential for controlling VSLs. [PERSON] et al. [17] proposed model predictive schemes based on MPC for traffic control in large freeway systems, and the performance of the proposed approach is assessed via simulation. [PERSON] et al. [18] proposed a local MPC with only one communication cycle at each sampling time. This controller improves the local controller performance, and although it is suboptimal concerning the centralized controller behavior, it can be implemented in real-time. [PERSON] et al. [19] proposed two novel MPC algorithms for coordinated control of discrete VSLs and continuous RM rates. The proposed algorithms use a distributed control architecture and an alternating optimization scheme to relax the MINLP optimization problems. [PERSON] et al. [20] focused on reducing the computation times of MPC for integrating variable speed limits and ramp metering. This was achieved through a parameterized control strategy that optimizes both the upstream and downstream boundaries of a speed-limited area and the parameters of the ALINEA ramp metering strategy. Additionally, there are several model-based optimization methods focused on VSL. [PERSON] et al. [21] used a modified cell transmission model (CTM) to model the traffic flow at the freeway bottlenecks under the VSL control. The VSL control factors were optimized by using the genetic algorithm. [PERSON] et al. [22] adopted the same model and controller, but lane-changing control was considered. [PERSON] et al.