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| In this talk we introduce a general way to construct a Boltzmann description of optimal control problems for large systems of interacting agents. The approach is applied to a constrained microscopic model of opinion formation. The main feature of the method is that, thanks to a model predictive approximation, the control is explicitly embedded in the resulting binary interaction dynamic. In particular in the so-called quasi invariant opinion limit simplified Fokker-Planck models can be derived which admit explicit computations of the steady states. The robustness of the controlled dynamics is illustrated by several numerical examples which confirm the theoretical results. Different generalizations of the presented approach are possible, like the introduction of the same control dynamic through leaders or the application of this same control methodology to swarming and flocking models. |
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