Control of multiscale model for social dynamics

We illustrate a multiscale model for social dynamics of large groups. The examples we have in mind span both cases of real dynamics, such as crowd in motion, but also virtual dynamics, such as opinion formation in social networks. The model is based on a measure theoretic approach, where the space of Radon measure with finite mass is endowed with a generalized Wasserstein metric. The latter allows the comparison of measures with different mass, thus including models in which the total mass of the measure may vary in time. The control paradigm is a centralized sparse control algorithm: A centralized controller is free to act on any agent of the system, but with the constraint of acting only on a small number of agents at the same time. We show some results in the completely discrete case and some new approach to deal with the continuum and mixed cases.