Stochastic Analysis Seminar – Ana Djurdjevac (University of Oxford)

We study collective behaviour in large systems of interacting stochastic agents, with a particular focus on flocking dynamics and optimal control problems. In the first part, we consider second order Cucker–Smale type models with inertia and derive reduced inertial PDE descriptions that retain the essential flocking mechanisms while significantly reducing complexity. These reduced models provide a foundation for a rigorous analysis of stability and long-time behaviour in alignment dynamics. This is a joint work with N. Conrad, F. Cornalba and S. Zimper,

In the second part, we address optimal control problems for interacting agent systems in opinion dynamics influenced by a fixed number of stochastic leaders. We study a partial mean-field limit, leading to a McKean–Vlasov equation for the followers coupled to controlled stochastic dynamics for the leaders. We show convergence of optimal controls from the finite-agent system to the meanfield limit and propose efficient numerical methods for computing leader-based controls. This is a joint work with N. Conrad, C. Hartmann, C. Schütte and S. Zimper