Adaptive stability boundary-based model predictive control for vehicle lateral stability under low-adhesion conditions

To address the nonlinear instability of vehicles under extreme operating conditions such as high speed, low road adhesion, and large steering angles, this paper establishes a lateral–yaw dynamics model considering tire nonlinear characteristics. The effects of longitudinal vehicle speed, front-wheel steering angle, and road adhesion coefficient on vehicle chaotic bifurcation behavior and phase-plane stability boundaries are analyzed. Based on a phase-plane point-set identification method, an adaptive stability region varying with operating conditions is constructed and transformed into a state constraint for model predictive control. Accordingly, a boundary-constrained model predictive control method incorporating nonlinear stability boundaries, referred to as BMPC, is proposed. In addition, the local stability of the system near equilibrium points is analyzed using the Lyapunov method. Co-simulation and hardware-in-the-loop test results demonstrate that the proposed BMPC method can effectively prevent the vehicle states from entering unstable regions. Under complex road conditions and extreme handling scenarios, the method achieves improved path-tracking accuracy, lateral stability, and robustness. The results provide theoretical support and engineering guidance for stability control of intelligent vehicles under complex driving conditions.