On the system of partial differential equations arising in mean field type control

Yves Achdou (1) , Mathieu Laurière (1)

1 LJLL - Laboratoire Jacques-Louis Lions

We discuss the system of Fokker-Planck and Hamilton-Jacobi-Bellman equations arising from the finite horizon control of McKean-Vlasov dynamics. We give examples of existence and uniqueness results. Finally, we propose some simple models for the motion of pedestrians and report about numerical simulations in which we compare mean filed games and mean field type control.

Mots clés: existence and uniqueness; mean field type control

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Analyse numérique [cs.NA]

Yves Achdou, Mathieu Laurière. On the system of partial differential equations arising in mean field type control. 2015. ⟨hal-01132008⟩