A mean-field game model for homogenous flocking

    •  Grover, P., Bakshi, K., Theodorou, E., "A mean-field game model for homogenous flocking", Chaos: An Interdisciplinary Journal of Nonlinear Science, DOI: 10.1063/​1.5036663, Vol. 28, No. 6, June 2018.
      BibTeX TR2018-032 PDF
      • @article{Grover2018jun,
      • author = {Grover, Piyush and Bakshi, Kaivalya and Theodorou, Evangelos},
      • title = {A mean-field game model for homogenous flocking},
      • journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
      • year = 2018,
      • volume = 28,
      • number = 6,
      • month = jun,
      • doi = {10.1063/1.5036663},
      • url = {}
      • }
  • Research Areas:

    Control, Dynamical Systems


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 homogenous flocking model for agents with intrinsic gradient-type 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 uncontrolled 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.