(Sub)Optimal feedback control of mean field multi-population dynamics

TL;DR

This paper develops a multiscale control approach for two-population agent models, using a Boltzmann approximation and sampling methods to derive sub-optimal controls, with applications in opinion dynamics.

Contribution

It introduces a novel multiscale control framework for multi-population dynamics, combining Boltzmann approximation and sampling to handle large-scale systems.

Findings

Effective control of opinion dynamics demonstrated

Sub-optimal control laws outperform baseline methods

Numerical experiments validate the approach

Abstract

We study a multiscale approach for the control of agent-based, two-population models. The control variable acts over one population of leaders, which influence the population of followers via the coupling generated by their interaction. We cast a quadratic optimal control problem for the large-scale microscale model, which is approximated via a Boltzmann approach. By sampling solutions of the optimal control problem associated to binary two-population dynamics, we generate sub-optimal control laws for the kinetic limit of the multi-population model. We present numerical experiments related to opinion dynamics assessing the performance of the proposed control design.