This paper investigates the lane keeping control for four-wheel independently actuated autonomous vehicles. To guarantee the vehicle safety when the active-steering motor entirely fails, the steering manoeuvre is realized by the differential drive assisted steering (DDAS) that is generated by the differential moment between the front wheels. A novel adaptive multivariable super-twisting control strategy is proposed to realize the control objective in finite time, considering the multiple unknown and mismatched disturbances of the steering system with the chattering effect removed. In the sliding surface, a nonlinear function is designed to adaptively change the damping ratio of the closed-loop system so as to improve the transient performance of the lane keeping control in the faulty steering condition. The controller design has avoided the use of the lateral velocity which is usually hard to measure in practice. Instead, the lane keeping errors and their time derivatives are estimated with a high-order sliding mode observer based on a vision system. The finite-time convergence of the closed-loop system is proved by the Lyapunov method. Results of CarSim-Simulink simulations with the proposed control strategy compared with a tradition sliding mode controller based on a high-fidelity and full-car model have verified the effectiveness and robustness of the proposed controller in the lane keeping control via DDAS with the guaranteed high performance.