# Vehicle Control Strategy Evaluation Based on the Driving Stability Region
## 1 Introduction  
When driving at high speeds or on low-adhesion road surfaces, due to the influences of steering or external interference, the lateral adhesion of the vehicle is prone to reaching its adhesion limit. The lateral velocity, yaw rate, and other state variables will increase sharply, causing the vehicle to lose dynamic stability and leading to traffic accidents. With the development of the vehicle industry [1] and increasing numbers of driver assistance systems, the complexity of the vehicle system increases, and the changeable weather, complex road conditions [2], diverse driving tasks, and dynamic driving conditions also present higher requirements for vehicle handling stability [3]. The vehicle dynamics control can control each state variable within the stable range and can further improve the safety of vehicles. Vehicle dynamics control plays an important role in the vehicle handling stability. Many scholars have carried out extensive research on the control strategies and methods to improve the handling stability of vehicles [4, 5] and confirmed the effectiveness of the control methods. However, due to the different control mechanisms and vehicle dynamics' models, there is no unified standard method for the evaluation and analysis of different control strategies. At present, in the research on stability regions of vehicles, different vehicle stability regions are defined according to the different research needs [6]. One typical vehicle stability region is based on state parameters, which are mainly obtained through two-dimensional phase plane analysis methods. [PERSON] et al. [7] and [PERSON] [8] proposed a method to evaluate the vehicle stability under steering motion and extreme steering conditions using the phase plane of the sideslip angle of the center of mass-sideslip angle derivative of the center of mass (\(\beta-\dot{\beta}\)), and suggested the \"double-line method\" stability criterion. However, this stability region is an open style. There are many unstable trajectories far from the focus point, and the boundary of the phase plane stability region is determined by many factors (for example, differences of models, vehicle parameters, and the uncertainty of the road friction coefficient). [PERSON] et al. [9] introduced the yaw rate threshold into the double-line method, coordinated the control of the sideslip angle of the center of mass and yaw rate, and designed the vehicle stability region combined with the double-line method and yaw rate method. [PERSON] et al. [10] proposed an improved five-eigenvalue diamond-shaped stability region division method based on the deficiency of the existing method for dividing the stable region of the phase diagram. According to the changing law of the phase diagram, the diamond-shaped stability region moving with the equilibrium point was selected as the stable region. This method mainly provided an accurate fundamental for the stability control strategy to intervene in the control. [PERSON] et al. [11] proposed a method to calculate the control domain based on the three-degree-of-freedom model, that is, in the state space of the control domain, the vehicle can finally transition to the initial state set of the system's stable equilibrium point through effective control strategies. The method verified the effectiveness of different vehicle safety-assisted driving systems, but it did not consider the influence of driving on handling stability. On the other hand, the stability region of the vehicle is usually analyzed from the perspective of control parameters. [PERSON] et al. [12] established a three-degree-of-freedom vehicle dynamics model with a nonlinear tire model, and estimated the stability region of the vehicle based on an energy method. This calculation method only provided a reference for determining the boundary of the stability region, but the specific stability region of the vehicle was not calculated in this paper. [PERSON] et al.