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

TL;DR

This paper investigates the behavior of multi-agent systems with nonlinear affine control dynamics as the number of agents approaches infinity, using mean-field and kinetic approaches to analyze optimal control strategies.

Contribution

It introduces a novel analysis of multi-agent systems' limits, combining mean-field and kinetic methods for optimal control with a finite number of leaders.

Findings

Mean-field limit analysis for controlling finite agents within large populations

Kinetic limit approach preserving the controlled agent percentage

Formulation of optimal control problems in both limits

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.