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

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.