Modeling Collective Behaviors: A Moment-Based Approach

• 成果类型: Article
• 署名作者: Zhang, Silun; Ringh, Axel; Hu, Xiaoming; Karlsson, Johan
• 署名单位: Massachusetts Institute of Technology (MIT); Hong Kong University of Science & Technology; Royal Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2976315
• 发表日期: 2021
• 页码: 33-48
• 关键词: Distributed parameter systems; large-scale systems; Method of moments; moment-based modeling; multiagent systems; reduced order systems; Systems modeling

摘要

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.