标题： 混合多种群交通流模型：均值场极限的最优控制 显示英文标题

标题： Hybrid multi-population traffic flow model: Optimal control for a mean-field limit

摘要： 建模异质和多车道交通流对于理解和控制复杂的交通系统至关重要。 在本工作中，我们考虑三种车辆群体：两类由人类驾驶的车辆（汽车和卡车）以及自动驾驶车辆，后者以受控加速度为特征。 与单群体模型相比，多群体建模面临更大的挑战，主要是由于描述换道行为所需的参数数量增加，以及在传递到平均场极限时的复杂性增加。 我们将多车道交通建模为一个混合动力系统，结合每条车道内的连续动力学和对应于换道操作的离散事件。 然后，我们从微观和介观角度对这种混合系统的最优控制问题进行公式化和分析。 使用 $\Gamma$-收敛技术，我们在有限维混合系统的平均场极限中证明了最优控制问题解的存在性。 最后，我们展示了数值模拟，说明卡车对整体交通效率的影响。 显示英文摘要

摘要： Modeling heterogeneous and multi-lane traffic flow is essential for understanding and controlling complex transportation systems. In this work, we consider three vehicle populations: two classes of human-driven vehicles (cars and trucks) and autonomous vehicles, the latter characterized by controlled acceleration. Compared to single-population models, multi-population modeling poses greater challenges, primarily due to the increased number of parameters required to describe lane-changing behavior and the added complexity in passing to the mean-field limit. We model multi-lane traffic as a hybrid dynamical system, combining continuous dynamics within each lane and discrete events corresponding to lane-changing maneuvers. We then formulate and analyze the optimal control problem associated with such hybrid systems from both microscopic and mesoscopic perspectives. Using techniques from $\Gamma$-convergence, we prove the existence of solutions to the optimal control problem in the mean-field limit of a finite-dimensional hybrid system. Finally, we present numerical simulations illustrating the impact of trucks on overall traffic efficiency.