Mean-field and kinetic limit of affine control systems: optimal control through leaders

Abstract

This paper studies a multi-agent system starting from a single agent dynamics which is a nonlinear affine control system. It analyze what happens when the number of agents goes to infinity using two different approaches, a granular mean-field one, trying to control only a finite number of agents while all the others goes to infinity, and a kinetic one, when in the limit the percentage of controlled agents is preserved. In both cases the optimal control problem starting from the solution for the finite dimensional one is stated.