## 1 Introduction  
Stop-and-go waves are a special traffic phenomenon that is well-known empirically, but it is a little difficult to describe them in traffic models. This is because there are disturbances in the traffic flow that typically arise. Stop-and-go waves are amplified due to the hysteresis effect of the acceleration and deceleration of the vehicle as they propagate upstream [1, 2]. Such irregular behavior in traffic flow can cause a series of traffic problems, such as congested traffic, increased fuel consumption, and even a potential safety hazard. Therefore, it is necessary to investigate the problem of traffic wave dissipation. Many empirical studies have been developed and expanded on how to improve the impact of traffic oscillation on traffic safety and traffic efficiency, and many theories and models have been used to explain the mechanism of traffic oscillation. The key to dissipating stop-and-go waves is to smooth traffic speed on both the temporal and spatial dimensions, by which a stabler and safer flow can be achieved [3]. In the early stage, control approaches using variable speed limits (VSLs) have been proposed, which can smooth the traffic flow speed, optimize the traffic flow, and avoid stop-and-go waves and other unstable states [4, 5, 6]. One notable example is SPECIALIST [7], using a controlled moving bottleneck to stop-and-go wave dissipation. However, the disturbance cannot be handled due to its feed-forward structure when the VSLs are activated with a demand increment. Some studies developed a model predictive control (MPC) approach of VSLs to resolve jam waves, where the design was based on extended cell transmission models and EulerianLighthill-Whitham and Richards (LWR) models [8; 9]. However, the performance of VSLs largely relies on the compliance rate and is limited to the installation location and number of variable message signs on the road. In recent years, with the advent of autonomous driving and communication technology, more precise and emerging control strategies have provided new ideas for improving traffic performance. Some studies have considered vehicle automation and communication systems, and a model-based quadratic programming problem has been developed to minimize traffic congestion [10; 11]. Many researchers concluded that cooperative ACC-equipped vehicles can detect and suppress stop-and-go waves [12]. Some researchers have experimentally demonstrated that autonomous vehicle (AV) driving algorithms can be specifically designed to dissipate stop-and-go waves and have created an automated vehicle control strategy called FollowerStopper (FS) [13; 14]. Interestingly, the results showed that FS can make the system more uniform, but it cannot increase the average velocity [15]. In connected and autonomous environments, some researchers have proposed a theoretical jam-absorption driving (JAD) strategy to eliminate traffic jams [16] and have derived the theoretical conditions for restricting secondary jams [17]. Additionally, a real-time control system for operating JAD against multiple moving jams was presented on freeway sections [18]. Similarly, some studies have proposed the JAD based on different car-following models to reduce traffic waves and improve traffic performance [19; 20; 21]. Some studies focus on guiding vehicle trajectories to enhance traffic performance. Taking into account fuel consumption and driving comfort, a piecewise trajectory optimization model was proposed to smooth the platoon of CAVs [22]. MPC has been widely used in traffic control due to its capability of solving multivariable optimization problems, systematically accounting for constraints on both state and control actions, and considering the anticipated future behavior of the system [23].