多车道多类交通混合系统的平均场极限
Mean-field limit of a hybrid system for multi-lane multi-class traffic
摘要：
本文主要研究车辆交通流激励下的耦合平均场方程和离散事件常微分方程。准确地说，多车道交通流中存在的人类驾驶和自动驾驶车辆被认为是，与自动驾驶车辆可能会受到外部政策制定者的影响。首先，基于连续Bando-Follow-the-Leader动力学与变道机动引起的离散事件耦合，建立了有限维混合动力系统。然后，严格推导了有限维混合系统的平均场极限，用于人驱动车辆的动力学。人类驾驶车辆的微观变道机动产生了一个源项的平均场PDE。这导致了一个无限维的混合系统，这是描述耦合Vlasov型PDE，常微分方程和离散事件。
英文摘要：
This article aims to study coupled mean-field equation and ODEs with discrete events motivated by vehicular traffic flow. Precisely, multi-lane traffic flow in presence of human-driven and autonomous vehicles is considered, with the autonomous vehicles possibly influenced by external policy makers. First a finite-dimensional hybrid system is developed based on the continuous Bando-Follow-the-Leader dynamics coupled with discrete events due to lane-change maneuvers. Then the mean-field limit of the finite-dimensional hybrid system is rigorously derived for the dynamics of the human-driven vehicles. The microscopic lane-change maneuvers of the human-driven vehicles generates a source term to the mean-field PDE. This leads to an infinite-dimensional hybrid system, which is described by coupled Vlasov-type PDE, ODEs and discrete events.
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