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A mean-field game model for homogeneous flocking
- Source :
- Chaos (Woodbury, N.Y.). 28(6)
- 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
- Subjects :
- 0209 industrial biotechnology
Mathematical optimization
Collective behavior
Population
FOS: Physical sciences
General Physics and Astronomy
Inverse
Systems and Control (eess.SY)
Dynamical Systems (math.DS)
02 engineering and technology
System of linear equations
37N35, 34C23, 37L15, 91A13, 91A10, 93E20
01 natural sciences
symbols.namesake
020901 industrial engineering & automation
FOS: Electrical engineering, electronic engineering, information engineering
FOS: Mathematics
Mathematics - Dynamical Systems
0101 mathematics
education
Mathematics - Optimization and Control
Mathematical Physics
education.field_of_study
Flocking (behavior)
Applied Mathematics
010102 general mathematics
Statistical and Nonlinear Physics
Optimal control
Nonlinear Sciences - Adaptation and Self-Organizing Systems
Optimization and Control (math.OC)
Nash equilibrium
Phase space
symbols
Computer Science - Systems and Control
Adaptation and Self-Organizing Systems (nlin.AO)
Subjects
Details
- ISSN :
- 10897682
- Volume :
- 28
- Issue :
- 6
- Database :
- OpenAIRE
- Journal :
- Chaos (Woodbury, N.Y.)
- Accession number :
- edsair.doi.dedup.....8e1fda351814fb7e679c0a2cf4047147