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Maintaining the curved path-tracking accuracy and stability of autonomous vehicles under various road conditions is a significant challenge in the field of vehicle control. To address this limitation, a curved path-tracking strategy under variable velocity based on the adaptive model predictive control (MPC) is proposed for autonomous vehicles. Through the analysis of the vehicle dynamics model, the theoretical basis is presented to improve the performance of the curved path tracking by changing the vehicle velocity, and the adaptive velocity (AV) planner is designed to generate variable velocities depending on the path curvature and road friction coefficients. In addition, the adaptive model predictive controller, which adopts the fuzzy inference system with vehicle velocity and path curvature as inputs to obtain the adaptive prediction horizon (APH), is employed to realize curved path-tracking and velocity control with actuator constraints by manipulating the steering angle of the front wheels and the longitudinal tire forces of the vehicle. In comparison with the control strategy with three other control strategies based on MPC algorithm via simulation experiments on the Simulink/CarSim platform, the curved path-tracking control strategy with AV and APH proposed in this paper exhibits satisfactory performance in terms of path-tracking accuracy and stability. [ABSTRACT FROM AUTHOR]