## 1 Introduction
Recently, some researchers have conducted a review of model predictive path tracking (PT) control for automated road vehicles [24], considering the following MPC methods for PT control: linear MPC [25; 26], linear time-varying MPC [27], linear parameter-varying MPC [28], nonlinear MPC [29], hybrid MPC [30], neural network MPC [31], robust MPC [32], and learning MPC [33]. Some researchers have proposed a learning-based model predictive control (LMPC) algorithm for a Formula Student (FS) autonomous vehicle to improve the dynamic model accuracy of the vehicle [34]. Some researchers have summarized the studies on learning-based MPC, focusing on the following three aspects [35]: (1) learning the system dynamics: taking into account the automatic adjustment of the system dynamic model [36], both during operation and between different operational instances; (2) learning the controller design: emphasizing the problem formulation [37; 38], such as defining cost functions, constraints, or terminal components, leading to improved closed-loop performance; (3) MPC for safe learning: decoupling the optimization of the objective function subject to constraint conditions [39]. To reduce traffic congestion and improve the safety of bottleneck areas, a dynamic speed control method was proposed using connected and autonomous vehicle (CAV) technology [40]. Based on the model predictive control (MPC) framework and safety potential field (SPF) model, an alternative CAV platoon dynamic control method was developed [41]. Some researchers proposed a multi-objective, guaranteed feasible connected and autonomous vehicle (CAV) platoon control method for signalized isolated intersections with priorities [42]. To capture hybrid traffic flow dynamics, an MPC model embedded with a mixed-integer nonlinear program was developed [43]. To optimize a vehicle platoon system in terms of car-following behavior, a decentralized MPC strategy for longitudinal velocity control was established [44]. Some researchers proposed a comprehensive linear time-varying MPC design for a type of AV to achieve good trajectory tracking in a practical driving scenario [45]. Some researchers proposed a model of predictive control based on ACC to dampen traffic waves and reduce traffic congestion [46; 47]. A safety-enhancing eco-driving strategy for CAVs based on a hierarchical distributed framework was proposed to optimize the trajectory of CAVs on a signalized arterial in mixed traffic flow [48]. A polytopic model-based robust predictive control scheme was proposed to construct the path tracking of AVs [49]. For the cooperative control system of CAVs, a distributed control architecture and hierarchical controller based on a multi-agent system (MAS) were proposed to handle complex traffic scenarios [50]. Some researchers have proposed a hierarchical model predictive control framework that can be used for the coordinated and integrated control of a motorway system to achieve traffic flow efficiency, considering that serval vehicles were equipped with specific vehicle automation and communication systems [51]. JAD is a behavior of mitigating traffic jams by dynamically changing the headway of a single vehicle and consists of two actions termed \"slow-in\" and \"fast-out\" [52]. The \"slow-in\" is the action to avoid being captured by a jam and to eliminate it by decelerating and creating a long space headway proactively. The \"fast-out\" is an action that follows the leading vehicle by quickly accelerating without unnecessary time intervals after the \"slow-in\". However, the JAD strategy focused on dissipating traffic waves without evaluating both traffic efficiency and traffic safety fully. To address the gap, this study develops an optimal control problem for JAD against traffic waves, which provides a good trade-off between traffic efficiency and traffic safety. More specifically, the optimal controller is established based on a microscopic car-following model formulated in a model predictive control (MPC) scheme.