A simultaneous trajectory tracking and stability control method is present for the four-wheel independent drive (4WID) automated vehicles to handle dynamic coupling maneuvers. To conquer the disadvantage that attendant disturbances caused by the dynamic coupling of traditional decentralized control methods degenerate the trajectory tracking accuracy, the proposed method takes advantage of the idea of decoupling to optimize the tracking performance. After establishing the dynamic model of the 4WID automated vehicles, the coupling mechanism of the vehicle dynamic control and its negative effect on trajectory tracking were studied at first. The inverse system model was then determined by machine learning and connected in series with the controlled object to form a pseudo linear system to realize dynamic decoupling. Finally, differing from previous tracking methods following the apparent lateral position and longitudinal velocity references, the pseudo linear system tracks the ideal intermediate targets transferred from the target trajectory, that is, the accelerations of vehicle in longitudinal, lateral and yaw directions, to indirectly achieve trajectory tracking and validly restrain the vehicle motion. The effectiveness of the proposed method, i.e., the high tracking accuracy and the stable driving performance, is verified through three coupling driving scenarios in the CarSim-Simulink co-simulations platform.