Neural-Network-Based Adaptive MPC Path Tracking Control for 4WID Vehicles Using Phase Plane Analysis

To improve the adaptability of 4WID electric vehicles under various operating conditions, this study introduces a model predictive control approach utilizing a neural network for adaptive weight parameter prediction, which integrates four-wheel steering and longitudinal driving force control. To address the difficulty in adjusting the MPC weight parameters, the neural network undergoes offline training, and the Snake Optimization method is used to iteratively optimize the controller parameters under diverse driving conditions. To further enhance vehicle stability, the real-time stability state of the vehicle is assessed using the β−β˙ phase plane method. The influence of vehicle speed and road adhesion on the instability boundary of the phase plane is comprehensively considered to design a stability controller based on different instability degree zones. This includes an integral sliding mode controller that accounts for both vehicle tracking capability and stability, as well as a PID controller, which calculates the additional yaw moment based on the degree of instability. Finally, an optimal distribution control algorithm coordinates the longitudinal driving torque and direct yaw moment while also considering the vehicle’s understeering characteristics in determining the torque distribution for each wheel. The simulation results show that under various operating conditions, the proposed control strategy achieves smaller tracking errors and more concentrated phase trajectories compared to traditional controllers, thereby improving path tracking precision, vehicle stability, and adaptability to varying conditions.