论文标题
非本地交通流模型的Lyapunov稳定
Lyapunov stabilization for nonlocal traffic flow models
论文作者
论文摘要
使用非本地二阶交通流模型，我们提出了一种控制稳定状态动力学的方法。该系统由以规定的速度驾驶的领先车辆控制，还决定了稳态。因此，我们考虑了显微镜和宏观尺度。我们表明，对于任何内核函数，微观交通流模型的固定点均无稳定。然后，我们介绍了微观和宏观尺度的Lyapunov功能，并计算出非本地术语影响固定溶液的明确速率。我们获得了恒定内核函数和任意初始数据或凹内核和单调初始数据的稳定效果。数值示例证明了理论结果。
Using a nonlocal second-order traffic flow model we present an approach to control the dynamics towards a steady state. The system is controlled by the leading vehicle driving at a prescribed velocity and also determines the steady state. Thereby, we consider both, the microscopic and macroscopic scales. We show that the fixed point of the microscopic traffic flow model is asymptotically stable for any kernel function. Then, we present Lyapunov functions for both, the microscopic and macroscopic scale, and compute the explicit rates at which the vehicles influenced by the nonlocal term tend towards the stationary solution. We obtain the stabilization effect for a constant kernel function and arbitrary initial data or concave kernels and monotone initial data. Numerical examples demonstrate the theoretical results.
