## 1 Introduction  
In today's society, with the rapid development of intelligent technology, the automobile industry is also developing rapidly. The number of cars is increasing, and the traffic environment is becoming more and more complex. As one of the critical technologies of autonomous driving, trajectory tracking performance should be superior. However, accuracy and vehicle stability need to be ensured during tracking. When the vehicle is on the ground with low adhesion or high speed, it often appears unstable. Ensuring vehicle stability under extreme conditions is a considerable challenge. Global scholars have conducted in-depth research on autonomous driving path tracking, such as PID control [1], fuzzy control [2], model predictive control (MPC) [3], sliding mode control (SMC) [4], and other methods, to design a tracking controller to track the reference trajectory and ensure tracking accuracy. MPC uses the current system state, the existing model, and the future control quantities to predict the future output of the system. MPC can solve the problems caused by the conventional path following control and accurately track the target path while considering the dynamic constraints of the vehicle [5, 6]. For example, [PERSON] et al. [7] designed a linear model predictive control strategy with soft constraints. The application principle of MPC in vehicle path tracking is to track the target path by establishing a vehicle dynamic model and considering various vehicle dynamic parameters. The front wheel angle or vehicle speed is used as a control variable. The control variables are optimized on a rolling basis,and the feedback correction is kept constant. Although these control algorithms can track the target path, some vehicle dynamic factors are not considered in the controller design process. For example, [PERSON] et al. [8] proposed a trajectory tracking method for uncrewed vehicles that combines model predictive and PID control. [PERSON] et al. [9] designed the MPC control method for the force-driven switching strategy based on the maximum tire lateral force and the zero moment method. SMC is one of the classical nonlinear control strategies capable of generating discontinuous control and moving the system along a predetermined sliding mode trajectory. Due to the variable structure property of sliding mode control, parameter uncertainties and disturbances do not affect the controller. At the same time, sliding mode control has the advantages of a fast response, a high accuracy, and strong robustness [10]. For example, [PERSON] et al. [11] proposed a lateral control system for active front wheel steering (AFS) and direct yaw moment control (DYC) based on second-order sliding mode control of the super-torsion pendulum, which reduces the chattering phenomenon of conventional sliding mode control. In addition, [PERSON] et al. [12] applied the extended disturbance observer to the sliding mode control so that the steering system had the feedforward compensation function. [PERSON] et al. [13] designed a new type of continuous sliding surface to reduce chattering. [PERSON] et al. [14] designed a non-singular terminal sliding mode control based on a recurrent neural network structure to improve the trajectory tracking performance. Compared with the traditional front wheel steering vehicle, the four-wheel steering technology has the vehicle's front and rear four wheels participate in the steering motion together, thus improving the handling stability of the vehicle in high-speed steering and the maneuvering flexibility in low-speed turning. Depending on its actuators, four-wheel steering technology can be divided into four-wheel active steering (4 WAS) and four-wheel independent steering (4 WIS). In these technologies, the driver controls the front wheel steering of 4 WS, according to the road conditions, and the rear wheel angle is determined by the vehicle state and the input of the front wheel driver through the controller.