## 1 Introduction  
In recent years, with the development of vehicle-to-everything (V2X) and sensor technologies, connected and automated vehicles (CAVs) received extensive attention regarding their ability to reduce the occurrence of traffic congestion and accidents [1]. Using environmental sensing sensors, such as cameras, lidar, and radar, the CAVs are able to obtain the state of roads and vehicles around them. The continuous development of V2X (vehicle-to-everything) technology has accelerated the development of the automobile intelligent network. V2X, including vehicle-to-vehicle (V2V), vehicle-to-infrastructure (V2I), and vehicle-to-pedestrians (V2P), enables each CAV to share information about the vehicle position, speed, acceleration, orientation, etc. with any traffic participating entity, which enhances the range of perception for these vehicles [2]. Equipped with perception systems and vehicular communications, a CAV acquires a wider range of information, which is beneficial for cooperative driving to evade crashes and achieve better traffic performance [3]. According to the intelligent degree of vehicles, vehicles are divided into six levels, from L0 to L5, by the Society of Automotive Engineers (SAE). By 2030, 82 million L4/L5 intelligent vehicles will be in operation in China, the United States, and Europe [4]. Despite the dramatic advances in autonomous driving, the predictable transition from purely conventional vehicles to a purely intelligent and connected environment will require a sustained investment in infrastructure and technology development. In the coming years, the transportation environment will exist in a transition stage of mixed transportation where the human-driven vehicles (HDVs) and CAVs coexist. In general, significant research regarding cooperative decision-making and control is under the assumption that all the vehicles on the road are CAVs [5; 6]. Cooperative decision-making and control in mixed traffic is a challenge in the field of intelligent transportation systems (ITSs) [7]. This is the reason why the CAVs need to interact with the HDVs, however the behavior of the HDVs is uncertain. To ensure a safe collaboration in mixed traffic environments, it is more practical to implement strategies for the CAVs that take the driver's behavior into account than expecting drivers to interact with the CAVs with caution. To imitate the human driving behavior, [PERSON] et al. developed an intelligent driver model (IDM) [8]. As a safe distance model, the IDM is able to describe the behavior of vehicles from free flow to congested flow with fewer parameters and reflects the dynamic changes of the vehicle position and speed in real time. [PERSON] et al. [9] modeled the HDVs using the IDM, which were guided by the CAVs to avoid collision and congestion and achieved a significant traffic efficiency. [PERSON] et al. [10] extended the IDM using the Ornstein-Uhlenbeck process to describe the perceptual error dynamically. [PERSON] et al. [11] proposed a model that combined a first principles nominal model with a Gaussian process model to predict human behaviors and then implemented a mixed platoon. However, the HDVs normally follow traffic rules to drive, rather than following the CAVs. Based on this view, the CAVs will anticipate the trajectories of the HDVs and cooperate to upgrade their safety and crossing efficiency in this paper. An unsignalized intersection scenario does not have traffic lights to govern it. The existence of conflict areas at the lane interchanges and the changes in the vehicle driving behaviors can easily cause disorder, resulting in traffic safety accidents, such as rear-end collisions and traffic jams, which is where a large number of accidents occur [12]. In this paper, we assumed that all the vehicles, including the HDVs, will be given the right of way according to the traffic regulations. Based on this assumption, the CAVs learned to adapt to the HDVs and cooperate with them for safe and efficient crossing.