Control Strategies for the Dynamics of Large Particle Systems

Abstract

We survey some recent approaches to control problems for large particle systems. Particle systems are transversal to many applications, ranging from classical physics to social sciences. The temporal evolution of the particles is determined by deterministic or stochastic dynamics and they are additionally able to optimize their trajectory over a large time. In particular, we investigate the limit of infinitely many particles leading to control of kinetic partial differential equations. To this goal a different notion of differentiability of the meanfield equation is introduced. Different mathematical methods based on meanfield games, model predictive control, and optimal control techniques will be discussed.