In this article we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the group of agents via their distribution and derive a method to estimate the dynamics of the moments. We use this to predict the evolution of the distribution of agents by first computing the moment trajectories and then use this to reconstruct the distribution of the agents. In the latter an inverse problem is solved in order to reconstruct a nominal distribution and to recover the macroscale properties of the group of agents. The proposed method is applicable for several types of multiagent systems, e.g., leader-follower systems. We derive error bounds for the moment trajectories and describe how to take these error bounds into account for computing the moment dynamics. The convergence of the moment dynamics is also analyzed for cases with monomial moments. To illustrate the theory, two numerical examples are given. In the first we consider a multiagent system with interactions and compare the proposed method for several types of moments. In the second example we apply the framework to a leader-follower problem for modeling a pedestrian crowd.

中文翻译：

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集体行为建模：基于时刻的方法


在本文中，我们介绍了一种使用矩对一组代理的集体行为进行建模和分析的方法。我们通过代理组的分布来表示代理组，并推导出一种估计力矩动态的方法。我们通过首先计算矩轨迹来预测智能体分布的演化，然后用它来重建智能体的分布。在后者中，解决逆问题以重建名义分布并恢复代理组的宏观特性。所提出的方法适用于多种类型的多智能体系统，例如领导者-跟随者系统。我们推导了力矩轨迹的误差范围，并描述了如何在计算力矩动力学时考虑这些误差范围。还针对单项矩的情况分析了矩动力学的收敛性。为了说明该理论，给出了两个数值示例。首先，我们考虑具有交互的多智能体系统，并针对几种类型的矩比较所提出的方法。在第二个示例中，我们将该框架应用于领导者-追随者问题，以对行人群体进行建模。