To optimize the mixed car-following behavior of connected autonomous vehicles (CAVs) and human-driven vehicles (HDVs), an adaptive backstepping sliding mode control (ABSMC) strategy for longitudinal velocity and distance control model (namely, MCF-ABSMCM) is put forth. First, the variable desired headway model (VDHM) is designed based on the vehicle-to-vehicle and vehicle-to-infrastructure information. Also, an asymmetric stochastic car-following model (ASCM) is designed to realistically describe the stochastic factor as well as vehicle acceleration and braking behaviors in mixed car-following. Second, an adaptive cruise sliding mode control law with a backstepping approach is devised to precisely track the desired following distance based on the VDHM. After creating the basic diagram of the two-model traffic flow, the intelligent driver model (IDM) is used as a baseline to compare and analyze the traffic capacity. Lastly, the effectiveness of the MCF-ABSMCM approach is confirmed in terms of both the mixed traffic flow density wave evolution and the vehicle control strategy, and the MCF-ABSMCM is validated under various adversary inputs. The simulation results demonstrate that the mixed-flow queue can finish headway tracking and keep a safe distance when using the MCF-ABSMCM described. This control strategy has been validated in VISSIM to significantly improve the efficiency of traffic operations compared to IDM and ASCM.
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