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The differential drive assist steering (DDAS) system improves the handiness of steering by torque difference between two-side wheels. However, the DDAS and the vehicle stability control (VSC) will interfere with each other due to the same actuators. This paper proposes a hierarchical coordination control approach for the DDAS and VSC. The system is divided into four layers: the parameter estimation layer, the control region division layer, the coordination decision layer, and the control allocation layer. In the control region division layer, the stable area is firstly determined on the $\beta - \dot{\beta }$ phase portrait, and the coordinated control region is obtained by applying the simulated annealing algorithm inwardly and outwardly to the boundary of the stable area. In the coordination decision layer, the direct control strategy of steering hand wheel torque is used to establish the controller of the DDAS based on the fuzzy adaptive PID algorithm. At the same time, the controller of yaw moment is established based on the sliding mode control theory. In the stable region, the DDAS works separately. The VSC works separately in the unstable region. In the coordination region, the Sigmoid function is used to adjust the weight coefficient of the DDAS dynamically. Besides, the control allocation layer includes torque distribution controller and vehicle slip ratio controller. Finally, the vehicle model is established in CarSim, the control strategy, and the wheel motor model are established in Simulink. The joint simulation results of several typical conditions show that the designed control strategy can improve the handling stability of the vehicle effectively while DDAS working even in severe driving condition. [ABSTRACT FROM AUTHOR]