Hopf bifurcation analysis and control of two-lane car-following model for connected vehicles with driver assistance systems

Connected vehicles (CVs) serve as an important connection from human-driven vehicles (HDVs) to pure connected autonomous vehicles, whose main function is to improve driver’s operation combined with driver assistance systems (DAS). By utilizing information shared on CVs, DAS is capable of automatically calculating and analyzing safe and efficient driving behaviors for drivers. However, drivers may operate by combining their personal thoughts with shared recommendation of DAS, which will usually result in a response time-delay. Therefore, the paper presents an innovative feedback control strategy that considers the driver’s visual angle response time-delay for the two-dimensional two-lane car-following model (TDTLCFM) combined with compliance rate of CVs drivers to DAS to optimize and improve DAS. Through the linear analysis and Hopf bifurcation analysis to obtain the stability conditions and equilibrium points of the traffic flow. And then designing the feedback controller to suppress traffic instability so as to suppress traffic bifurcation caused by driver’s response time-delay. Finally, numerical simulation was conducted on 100 vehicles, and the simulation results show that the controller can effectively suppress traffic congestion without changing the equilibrium point, significantly improving traffic efficiency and stability. At the same time, numerical simulations of heterogeneous traffic flow composed of HDVs and CVs indicate that the stability of mixed flows varies with the market penetration rate of CVs, the higher the market penetration rate, the stronger the anti-interference ability of the mixed flow.