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.

Mean-field optimal control as Gamma-limit of finite agent controls

Savare', Giuseppe
;
2019

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 Γ-convergence argument constructed over the mean-field limit, which stems from leveraging the superposition principle.
2019
Savare', Giuseppe; Lisini, Stefano; Orrieri, Carlo; Fornasier, Massimo
File in questo prodotto:
File Dimensione Formato  
1803.04689.pdf

accesso aperto

Descrizione: Preprint pubblicato su ArXiv
Tipologia: Documento in Pre-print (Pre-print document)
Licenza: Creative commons
Dimensione 409.5 kB
Formato Adobe PDF
409.5 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11565/4032536
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 23
  • ???jsp.display-item.citation.isi??? 18
social impact