Mean-field optimal control with stochastic leaders

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.

numerical analysisoptimization and control

Audience: researchers in the topic

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CAM seminar

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