Phase transitions and congestion of heterogeneous lattice hydrodynamics model considering delayed difference feedback control in connected autonomous vehicles environment

With the sustainable development of artificial intelligence technology and vehicle-road collaboration technology, the intelligent connected automobile has become one of the hot topics in current transportation system all over the world. In the connected autonomous vehicles environment, traffic flow can run more efficiently, which will alleviate traffic congestion and reduce delays of human factors. To explore feedback control effect of delayed difference for different types of vehicles, we design a new heterogeneous lattice hydrodynamic model including connected autonomous vehicles and human-driven vehicles. As demonstrated by the linear stability analysis, it is evident that both the penetration ratio of connected autonomous vehicles and delayed reaction time of heterogeneous vehicles have an undeniable impact on traffic flow stability. Furthermore, according to the nonlinear analysis based on the approximate perturbation theory, we derive the modified mKdV equation as well as the kink-antikink density wave solution. Finally, the spatiotemporal density evolution and hysteresis loop are drawn via numerical simulation. From numerical simulation, the density variation and the hysteresis loop is gradually reduced with the increase of the penetration ratio of connected autonomous vehicles in heterogeneous vehicles, which indicates that the penetration ratio of connected autonomous vehicles can effectively enhance the stability of traffic flow in the human-driven and connected autonomous vehicles environment. In addition, as the delayed reaction time of both connected autonomous vehicles and human-driven vehicles decreases, traffic flow becomes more stable. This discovery is of great significance to optimize the design and application of intelligent connected vehicle system, and helps to improve road traffic efficiency and safety.