基于时滞反馈的ARZ交通流模型的入口匝道控制

On ramp control of ARZ traffic flow model based on time-delay feedback

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。

For the Aw-Rascle-Zhang(ARZ)non-equilibrium traffic flow model,if the traffic flow at the entrance is constant and the density of the traffic flow at the exit is constant,the system is in critical stability and there will be continuous oscillations near the equilibrium state.This article proposes the design of a time-delay feedback control strategy at the entrance ramp,and characterizes the time-delay term with the solution of the initial value problem of the first-order transportation equation,establishing the form of an infinite dimensional coupled closed-loop system for PDE-PDE.The operator semigroup theory is used to prove the well posedness of the system.The conclusion of exponential stability of the system is obtained by constructing a weighted strict Lyapunov function.The results indicate that when the feedback gain and delay values satisfy certain inequality constraints,the system energy reaches exponential decay.Finally,through numerical simulation,the effectiveness of the designed time-delay controller and the feasibility of parameter conditions are verified.