Stabilization of Stop-and-Go Waves in Vehicle Traffic Flow

• 成果类型: Article
• 署名作者: Zhang, Liguo; Luan, Haoran; Zhan, Jingyuan
• 署名单位: Beijing University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3337703
• 发表日期: 2024
• 页码: 4583-4597
• 关键词: Electric shock; Vehicle dynamics; Shock waves; roads; Numerical models; mathematical models; Feedback control; Aw-Rascle-Zhang (ARZ) traffic flow model; Boundary stabilization; coupled partial differential equations (PDE-PDE) system; Lyapunov function; stop-and-go waves

摘要

This article investigates the stabilization problem of stop-and-go waves in vehicle traffic flow with bilateral boundary feedback control. The stop-and-go waves induce the discontinuities of vehicle speed and density, which inturn lead to different traffic states on the front and back sides of the shock front. According to the Rankine-Hugoniot condition, a propagation equation of the shock front is proposed depending on the characteristic velocities of the Aw-Rascle-Zhang traffic flow model. Then, the complete dynamics of the stop-and-go waves is formulated as a coupled hyperbolic partial differential equations (PDE- PDE) system with a common moving boundary. The well posedness of the coupled system with the moving boundary is established via the fixed-domain method. To stabilize the discontinuous traffic state and the location of shock front simultaneously, the bilateral boundary feedback control is formulated for the stop-and-go waves of traffic flow. Some sufficient conditions in terms of matrix inequalities are derived for ensuring the local exponential stability of the closed-loop system in the H-2-norm. Finally, the theoretical results are illustrated with numerical simulations.