Traffic flow bifurcation control of autonomous vehicles through a hybrid control strategy combining multi-step prediction and memory mechanism with PID

•A new car-following model is proposed to describe the dynamic behavior of autonomous vehicle.•The bifurcation characteristic of traffic flow composed of autonomous vehicle is analyzed.•A controller that considers multi-step memory and multi-step prediction effect is designed.•A hybrid control strategy is proposed, which combines multi-step prediction and memory mechanism with PID. This paper is committed to capturing the dynamic behaviors of homogenous flow of autonomous vehicles (AVs), and exploring the control strategies to improve traffic conditions, which can alleviate traffic congestion and improve traffic efficiency. Firstly, a car-following model of AVs considering real-time driving state is established. Secondly, based on bifurcation theory and stability theory, bifurcation analysis is carried out and the relationship between bifurcation and stability is revealed. In order to suppress the bifurcation and improve the stability, a controller considering multi-step prediction and memory mechanism (MPM) is designed, and the root trajectories for eigenvalues and stable time length of the model controlled by MPM controller are calculated. In response to the limitations of the MPM controller, a hybrid controller including the MPM controller and PID controller is further proposed, and it is found that the model controlled by hybrid controller has greater range of stable bifurcation parameter and stable time length, which means better ability of bifurcation suppression. Finally, the capabilities of the controller proposed in this paper are effectively demonstrated by numerical experiments in MATLAB and simulation experiments in the ROS-Gazebo environment.