《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (10): 64-73, 88.doi: 10.6040/j.issn.1671-9352.0.2023.328
王一言(
),赵东霞*(),高彩霞
Yiyan WANG(),Dongxia ZHAO*(),Caixia GAO
摘要：
对于Aw-Rascle-Zhang(ARZ)非平衡交通流模型，若入口处的交通流量恒定，出口处交通流的密度恒定，则系统处于临界稳定，在平衡状态附近会有持续的振荡。提出在入口匝道处设计时滞反馈控制策略，并将时滞项用一阶运输方程初值问题的解进行刻画，建立了PDE-PDE无穷维耦合闭环系统的形式。采用算子半群理论证明系统的适定性。构造加权严格Lyapunov函数得到系统指数稳定的结论。结果表明，当反馈增益和时滞取值满足某个不等式约束条件时，系统能量达到指数衰减。最后，通过数值仿真，验证所设计时滞控制器的有效性和参数条件的可行性。
中图分类号:
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