## 1 Introduction  
The adaptive cruise control (ACC) system [1, 2] mainly senses the surrounding environment of the vehicle and automatically adjusts its speed to maintain a safe distance from the leader vehicle, thereby reducing the workload of the driver and improving driving safety and traffic flow. It has received widespread attention from researchers and car companies [3, 4]. While the ACC methodology primarily depends on being model-centric, achieving precise vehicle modeling poses challenges [5, 6]. This stems from the intricate hydrodynamics of vehicles, uncertainties, and the effects from both internal apparatus and external surroundings [7, 8]. Hence, it is often unfeasible to perfectly represent a vehicle's dynamics. Given this, the prevailing model-centric ACC techniques tend to employ a generic vehicle model. Notably, ACC development often utilizes nonlinear predictive control tailored to this general model [9, 10]. Moreover, when one linearizes the nonlinear equation dictating the vehicle's longitudinal motion, they can design ACC systems anchored in Proportional-Integral (PI), Proportional-Integral-Derivative (PID), \(H_{\infty}\), and sliding-mode structures. However, such designs presuppose a precise vehicle model. For example, to enhance control outcomes when dealing with indeterminate vehicle parameters, adaptive control methods are applied in the ACC design [11]. Should one need to create ACC systems for vehicles affected by unidentified nonlinear resistances and external factors, they might turn to estimation-centric methods. These often harness fuzzy logic or neural networks [12]. For instance [12], leveraged a fuzzy framework to mimic the lead car's model, while a predictive control strategy for the ACC was crafted using neural network methodologies. Despite the plethora of methodologies introduced, certain challenges persist. During the past decades, the existing ACC was mainly based on PID [13], linear quadratic form optimal control [14], model predictive control (MPC) [15], fuzzy /neural network control [12], sliding-mode control [16], and other control algorithms. PID has the advantages of a simple structure and no need for vehicle models, while MPC has the advantages of handling multiple constraints, which has been widely studied. Although traditional PID-based ACC can achieve the automatic control of vehicles, it cannot guarantee safety and has certain limitations in operating scenarios and opening conditions. [PERSON] et al. [17] used intelligent PI feedback/feedforward control methods to design adaptive cruise controllers. [PERSON] et al. [18] designed an ACC controller using the PID algorithm and participated in the Grand Collaborative Driving Challenge held in Helmand, Netherlands. ACC based on MPC can achieve automatic control with constraints, mainly used to solve problems, such as vehicle state constraints and energy consumption optimization [19; 20]. [PERSON] et al. [21] designed a dual-mode MPC adaptive cruise controller to achieve switching control between vehicle speed and distance. [PERSON] et al. [22] constructed an ACC control algorithm based on the MPC framework and designed an objective function based on fuel consumption and the driver's expected response. This method not only meets the driving characteristics of the driver but also improves the fuel economy and tracking ability. [PERSON] et al. [23] proposed a vehicle controller with variable acceleration for comfort and safety based on MPC, as well as an emergency controller to ensure safety when MPC is not functioning. The ACC controller based on MPC needs to establish an accurate vehicle dynamics model. However, due to the influence of road, weather conditions, and other factors, it is difficult to describe the relationship between the various actuators of the vehicle; this further makes the accurate vehicle driving-resistance model hard to construct. Generally, researchers use a simplified model of the vehicle [24].