Decentralized Convergence to Nash Equilibria in Constrained Deterministic Mean Field Control
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Date
2016-11
Publication Type
Journal Article
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yes
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Abstract
This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and influenced by the aggregate behavior of the overall population. For such large-scale systems, the theory of aggregative and mean field games has been established and successfully applied in various scientific disciplines. While the existing literature addresses the case of unconstrained agents, we formulate deterministic mean field control problems in the presence of heterogeneous convex constraints for the individual agents, for instance arising from agents with linear dynamics subject to convex state and control constraints. We propose several model-free feedback iterations to compute in a decentralized fashion a mean field Nash equilibrium in the limit of infinite population size. We apply our methods to the constrained linear quadratic deterministic mean field control problem.
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published
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Journal / series
Volume
61 (11)
Pages / Article No.
3315 - 3329
Publisher
IEEE
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Software
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Subject
Population control; Mean field games; Noncooperative agents; Large-scale systems
Organisational unit
03751 - Lygeros, John / Lygeros, John
08814 - Smith, Roy (Tit.-Prof.) (ehemalig) / Smith, Roy (Tit.-Prof.) (former)