Exponential stability of ARZ traffic flow model based on $ 2\times 2 $ variable-coefficient hyperbolic system

• DOI: 10.3934/math.2025026
• Publication Date: 2025-01-11T03:45:53Z
• Authors: Yiyan Wang; Dongxia Zhao; Caifen Sun; Yaping Guo
• Keywords: exponential stability; QA1-939; traffic flow model; boundary feedback control; lyapunov function; variable-coefficient hyperbolic system; Mathematics

<p>This paper studies the exponential stability of Aw-Rascle-Zhang (ARZ) traffic flow model. Given that steady state may be non-uniform, we obtain a $ 2\times2 hyperbolic system with variable coefficients. Then, by combining ramp metering and speed limit control, deduce kind proportional boundary feedback controller. The well-posedness closed-loop is proved using theory semigroups operators. Moreover, novel Lyapunov function, whose weighted function constructed solution first-order ordinary differential equation, can used for analysis. analysis gives sufficient condition parameters, which easy to verify. Finally, effectiveness control feasibility parameters are obtained numerical simulation.</p>