群体动力学中的一阶平均场对策
First order mean field games in crowd dynamics
摘要：
在本文中，我们研究了一个二维人群模型，行人速度由两个元素组成：一个非局部相互作用项，模拟其他步行者对每个人的影响，和控制项。后一项可以由行人选择，使得他们的最终路径是最优的w.r.t.合适的成本标准。假设行人可以预测他们的选择对整个人群的演变的影响，这是很自然的考虑耦合的连续性方程的平均场系统，它描述了行人密度的演变，与最优化问题的HJB方程。我们表明，这样的耦合系统承认解决方案，我们解释的解决方案中的行人模型。我们还将这一结果扩展到多个行人群体存在于环境中的情况，每个人都有自己的目标。
英文摘要：
In this paper we study a two dimensional crowd model where pedestrian velocity consists of two elements: a non--local interaction term, modeling the effect of other walkers on each individual, and a control term. This latter term can be chosen by pedestrians so that their resulting path is optimal w.r.t. a suitable cost criterion. Under the assumption that pedestrians can forecast the effect of their choices on the evolution of the whole crowd, it is natural to consider a mean field system coupling the continuity equation, which describes the evolution of the density of pedestrians, with the HJB equation for the optimization problem. We show that such coupled system admits solution and we interpret the solution in terms of the pedestrian models. We also extend this results to the case where multiple populations of pedestrians are present in the environment, each with his own objectives.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
