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 Î"-convergence argument constructed over the mean-field limit, which stems from leveraging the superposition principle.
Mean-field optimal control as Gamma-limit of finite agent controls / Fornasier, Massimo; Lisini, S.; Orrieri, C.; Savare, G.. - In: EUROPEAN JOURNAL OF APPLIED MATHEMATICS. - ISSN 0956-7925. - 30:6(2019), pp. 1153-1186. [10.1017/S0956792519000044]
Mean-field optimal control as Gamma-limit of finite agent controls
Fornasier, Massimo;Orrieri C.;
2019-01-01
Abstract
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 Î"-convergence argument constructed over the mean-field limit, which stems from leveraging the superposition principle.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione