Modeling collective behaviors: A moment-based approach

TL;DR

This paper introduces a moment-based modeling approach for analyzing collective behaviors in multi-agent systems, enabling prediction and reconstruction of group distributions with error bounds and convergence analysis.

Contribution

It presents a novel method to estimate and analyze the dynamics of agent distributions using moments, applicable to various multi-agent systems including leader-follower models.

Findings

Accurate prediction of agent distribution evolution.

Effective reconstruction of macro-scale group properties.

Validated approach through numerical examples.

Abstract

In this work 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 macro-scale properties of the group of agents. The proposed method is applicable for several types of multi-agent 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 multi-agent system with interactions and compare the proposed methods for several types of moments. In the second example we apply the framework to a leader-follower problem for modeling pedestrian crowd dynamics.