# Vehicle Control Strategy Evaluation Based on the Driving Stability Region
## 1 Introduction
[13] proposed a method to solve the vehicle stability region based on the dynamic bifurcation characteristics of dissipative energy, which provided a dynamic fundamental for the global dynamic analysis of the vehicle plane motion system. However, the influence of control strategy on the vehicle system dynamics was not studied. Aiming at the shortage of the plane stability domain in evaluating vehicle stability, an estimation method of the bus spatial stability domain was proposed by [PERSON] et al. [14]. Based on the quadratic energy function of the vehicle system, the bus spatial stability domain was determined by the Lyapunov method and the vehicle system stability characteristics. The research results show that the vehicle stability region determined by the above methods can effectively characterize the stability of the vehicle system. The above research has played a positive role in the control strategy evaluation of vehicle handling stability. However, research on the driving stability region of a vehicle is mostly focused on the stability region composed of vehicle state variables and steering control parameters. Research on the driving stability region is still in its early stages. Moreover, unified evaluation indexes are not incorporated when the aforementioned research evaluates the control effect of the vehicle handling stability. Different researchers choose different evaluation indexes according to their own research needs. There is a significant limitation to evaluating the effectiveness of vehicle stability control strategies by a single evaluation index. It is also difficult to determine the specific impact of control strategies on the overall stability of vehicle systems using different evaluation indexes together. Although the boundary of the stability region is clearly deduced by some research [15], intuitive and simple descriptions are still lacking in the practical engineering application process, for example, the combination of the physical meaning of the dynamic equilibrium point of the vehicle system, the driving stability region of pure control parameters composed of driving torque, and the front wheel steering angle is proposed in this paper. This is different from the bifurcation characteristics composed of state variables and control parameters. The accurate solution of the equilibrium points of high-dimensional nonlinear vehicle systems is achieved through a hybrid algorithm of GA + SQP, ensuring the accuracy of the equilibrium point solution. The neighborhood optimization in the algorithm ensures wider applicability for solving the equilibrium points of different high-dimensional systems, resulting in a more accurate driving stability region. The typical control strategies (the four-wheel steering system (4 WS) and direct yaw moment control (DYC)) were evaluated using the driving stability regions obtained under different control strategies. The results show that the control effect of DYC is better than that of 4 WS. The driving stability region has more intuitive engineering significance, providing a unified standard for accurately evaluating the control effect of vehicle handling stability under different control strategies. This provides the dynamic fundamental for integrated control and a safe driving assistance system design.