Bifurcation analysis of mixed traffic system with different car-following modes and distributed PID control strategy based on particle swarm optimizer

Abstract

This paper is committed to capturing the dynamical behaviors of the mixed traffic flow which is composed of human-driven vehicle (HDV) and connected autonomous vehicle (CAV), and exploring targeted control strategies to alleviate traffic congestion. Firstly, a novel car-following model is proposed for mixed traffic flow, which considers different car-following modes and functional degradation. Secondly, the bifurcation and stability analysis of proposed model are conducted to explore the occurrence of bifurcation in mixed traffic flow under different market penetration rate (MPR) of CAV and car-following mode ratio (CFR) of mixed flow, and numerical simulation is used to validate the conclusions of theoretical analysis. Thirdly, a modified distributed PID controller is proposed to suppress the bifurcation, and the particle swarm optimization (PSO) algorithm is used to optimize the control gains of the PID controller. The analysis results of controlled model verify the advantage of the controller, and the numerical simulation also confirms the conclusions. This paper can enrich the research on the characteristics of traffic flow, improve the theoretical basis of traffic control, and provide implications for traffic management.