Multiscale Modeling &Simulation, Volume 19, Issue 2, Page 589-611, January 2021.
We study the derivation of generic high order macroscopic traffic models from a follow-the-leader particle description via a kinetic approach. First, we recover a third order traffic model as the hydrodynamic limit of an Enskog-type kinetic equation. Next, we introduce in the vehicle interactions a binary control modeling the automatic feedback provided by driver-assist vehicles and we upscale such a new particle description by means of another Enskog-based hydrodynamic limit. The resulting macroscopic model is now a generic second order model (GSOM), which contains in turn a control term inherited from the microscopic interactions. We show that such a control may be chosen so as to optimize global traffic trends, such as the vehicle flux or the road congestion, constrained by the GSOM dynamics. By means of numerical simulations, we investigate the effect of this control hierarchy in some specific case studies, which exemplify the multiscale path from the vehiclewise implementation of a driver-assist control to its optimal hydrodynamic design.

中文翻译：

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驾驶辅助车辆对通用二阶交通模型的多尺度控制

多尺度建模与仿真，第 19 卷，第 2 期，第 589-611 页，2021 年 1 月。
我们通过动力学方法研究了从跟随领导者粒子描述中推导出通用高阶宏观交通模型。首先，我们将三阶交通模型恢复为 Enskog 型动力学方程的水动力极限。接下来，我们在车辆交互中引入了一种对驾驶员辅助车辆提供的自动反馈进行建模的二进制控制，并且我们通过另一个基于 Enskog 的流体动力学限制来升级这种新的粒子描述。由此产生的宏观模型现在是一个通用的二阶模型 (GSOM)，它又包含一个从微观相互作用继承的控制项。我们表明可以选择这样的控制来优化全局交通趋势，例如受 GSOM 动力学约束的车辆流量或道路拥堵。通过数值模拟，