On the system of partial differential equations arising in mean field type control
This work provides theoretical and numerical insights for researchers in mean field control theory, but it is incremental as it builds on existing frameworks without introducing a new paradigm.
The paper discusses the system of Fokker-Planck and Hamilton-Jacobi-Bellman equations for finite horizon control of McKean-Vlasov dynamics, providing existence and uniqueness results and comparing mean field games and mean field type control through pedestrian motion simulations.
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.