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A mean-field game model for homogeneous flocking
- Source :
- Chaos 28, 061103 (2018)
- Publication Year :
- 2018
-
Abstract
- Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game model whose behavior mimics an empirically derived non-local homogeneous flocking model for agents with gradient self-propulsion dynamics. The mean-field game framework provides a non-cooperative optimal control description of the behavior of a population of agents in a distributed setting. In this description, each agent's state is driven by optimally controlled dynamics that result in a Nash equilibrium between itself and the population. The optimal control is computed by minimizing a cost that depends only on its own state, and a mean-field term. The agent distribution in phase space evolves under the optimal feedback control policy. We exploit the low-rank perturbative nature of the non-local term in the forward-backward system of equations governing the state and control distributions, and provide a linear stability analysis demonstrating that our model exhibits bifurcations similar to those found in the empirical model. The present work is a step towards developing a set of tools for systematic analysis, and eventually design, of collective behavior of non-cooperative dynamic agents via an inverse modeling approach.<br />Comment: Revised to incorporate reviewers' suggestions. Accepted to Chaos journal
Details
- Database :
- arXiv
- Journal :
- Chaos 28, 061103 (2018)
- Publication Type :
- Report
- Accession number :
- edsarx.1803.05250
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1063/1.5036663