American Institute of Mathematical Sciences

September  2015, 35(9): 3879-3900. doi: 10.3934/dcds.2015.35.3879

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

 1 Université Paris Diderot, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS, Sorbonne Paris Cité F-75205 Paris, France

Received  May 2014 Revised  September 2014 Published  April 2015

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.
Citation: Yves Achdou, Mathieu Laurière. On the system of partial differential equations arising in mean field type control. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 3879-3900. doi: 10.3934/dcds.2015.35.3879
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