Computational and Applied Mathematics seminar

Abstract: We study optimal control problems for interacting agent systems arysing in opinion dynamics, where a large number of agents is influenced by a fixed number of stochastic leaders. We consider a partial mean-field limit, leading to a McKean–Vlasov equation for the followers coupled to controlled stochastic dynamics for the leaders. We show that optimal controls for the finite-agent system converge to the optimal control of the limiting mean-field system, providing a low-dimensional and computationally efficient approximation of high-dimensional control problems. In addition, we propose efficient numerical methods for computing leader-based controls. We illustrate the theoretical results with numerical experiments for the Hegselmann–Krause opinion dynamics model. This is joint work with N. Conrad, C. Hartmann, C. Schütte and S. Zimper.