# Game Theory-Based Interactive Control for Human-Machine Cooperative Driving
## 1 Introduction
A brain emotional learning circuit model (BELCM) was designed in [15] to simulate driver steering behavior, but it did not consider human-vehicle interaction. In terms of shared longitudinal control in an HSCV, the main contribution of this research direction focuses on using the haptic accelerator to perform vehicle following tasks [16; 17]. In particular, the integrated control framework of driver steering control and speed control models in HSCVs requires more research. For automation control systems, it is necessary to design shared controllers to assist drivers in driving safely and smoothly and to make timely interventions in dangerous situations. And there are a variety of shared controllers in HSCVs, which include a linear quadratic regulator (LQR) [18], Takagi-Sugeno (T-S) fuzzy control [11], \(\mathcal{H}_{\text{inf}}\) control [19], and MPC [20]. Compared with the above controller, MPC has the advantage of being suitable for solving multi-constraint and multi-variable optimization problems, and it has received widespread attention in the design of shared controllers for HSCVs [4; 6; 21]. In 2013 [22], [PERSON] et al. used constrained MPC to design a shared controller and then used a weighted summation method to integrate the control commands of the driver and the automation control system. However, this method ignored the adaptability of the shared controller to the driver's control input. A novel shared controller is designed in [20; 23], in which the driver's control commands are integrated into the MPC's cost function to form an optimization problem. Considering that the driver's unreasonable operation will pose a safety threat to the vehicle, [PERSON] et al. [24] added a driving control authority allocation strategy based on fuzzy logic in the shared controller. Another reference-free shared control framework based on MPC was designed by [PERSON] et al. [25]. In this shared controller, constrained Delaunay triangles and collision time are used to determine the safe area, vehicle sideslip angle, and yaw angular rate, which are used to design stability constraints. [PERSON] et al. [26; 27] use a non-cooperative MPC method to simulate the interaction between the driver and the controller, in which the driver steering controller and the automation controller need to minimize the cost function of cumulative trajectory errors while also considering the impact of their control outputs on each other. The above studies on shared controllers in HSCVs mainly focus on obstacle avoidance and lane keeping scenarios. However, previous research mentioned above on HSCV shared controllers focused primarily on static driving environments, such as safe avoidance of static obstacles on the road or lane keeping on a road without other vehicles, and it lacks consideration of the impact of complex factors such as vehicle interaction. In the complex traffic environment of the future, it will be necessary for HSCVs to share the road with adjacent traffic participants. Some research on how to design a safe and effective control scheme for HSCVs to avoid SVs or static obstacles safely was conducted. In [20], a method was demonstrated that integrates driver control commands into a constrained MPC and defines an environmental envelope and a stable handling envelope in the shared controller to ensure safe and stable obstacle avoidance driving. In [28], the elliptical driving safety field is used to design a strategy to avoid surrounding vehicles for human-machine shared control. [PERSON] et al. [29] developed a spatial collision risk system that allocates driving authority between the driver and the automation system to avoid surrounding vehicles. In [27], MPC and game theory are used to simulate the impact of the interaction between the driver and the automation system in obstacle avoidance scenarios. However, the status of obstacles or surrounding vehicles (SVs) is static or determined in the above studies while ignoring the influence of the behavioral changes of SVs.