Mean-field optimal control as Gamma-limit of finite agent controls
By Massimo Fornasier, S. Lisini, Carlo Orrieri, Giuseppe Savar'e. European journal of applied mathematics, 2018
71 citations recorded by the source corpus.
This paper focuses on the role of a government of a large population of interacting agents as a meanfield optimal control problem derived from deterministic finite agent dynamics. The control problems are constrained by a Partial Differential Equation of continuity-type without diffusion, governing the dynamics of the probability distribution of the agent population. We derive existence of optimal controls in a measure-theoretical setting as natural limits of finite agent optimal controls without any assumption on the regularity of control competitors. In particular, we prove the consistency of mean-field optimal controls with corresponding underlying finite agent ones. The results follow from a Γ -convergence argument constructed over the mean-field limit, which stems from leveraging the superposition principle.
Subfields: Computer Networks and Communications, Modeling and Simulation, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/d5a28455d6ae00d6e05b44a9037d8dcf37643756
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In Computer Networks and Communications
In Modeling and Simulation
Citations in the corpus
- A Pontryagin Maximum Principle in Wasserstein spaces for constrained optimal control problems (2018, unknown): “The existence of optimal solutions has been investigated with various degrees of generality in [1, 2, 34, 35, 33, 48], mostly by means of Γ-convergence arguments.”
- Differential inclusions in Wasserstein spaces: The Cauchy-Lipschitz framework (2020, background): “While a few results have been dealing with controllability properties of continuity equations [36, 37], the major part of the literature has been devoted to the study of optimal control problems, with contributions ranging from existence results [23, 38, 39, 40] and necessary optimality conditions [”