Mean-field control and Riccati equations

Michael Herty, Lorenzo Pareschi, Sonia Steffensen
(Network and Heterogeneous Media, 10, 2015, 699-715)

We present a control approach for large systems of interacting agents based on the Riccati equation. If the agent dynamics enjoys a strong symmetry the arising high dimensional Riccati equation is simplified and the resulting coupled system allows for a formal mean--field limit. The steady--states of the kinetic equation of Boltzmann and Fokker Planck type can be studied analytically.
In case of linear dynamics and quadratic objective function the presented approach is optimal and is compared to the model predictive control approach introduced in [2].