A Parabolic Approach to the Control of Opinion Spreading
We analyse the problem of controlling to consensus a nonlinear system modelling opinion spreading. We derive explicit exponential estimates on the cost of approximately controlling these systems to consensus, as a function of the number of agents N and the control time horizon T. Our strategy makes use of known results on the controllability of spatially discretised semilinear parabolic equations. Both systems can be linked through time rescaling.
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This work has been partially funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No 694126-DyCon), grant MTM2017-92996 of MINECO (Spain), the Marie Curie Training Network “Conflex”, the ELKARTEK project KK-2018/00083 ROAD2DC of the Basque Government, ICON of the French ANR and “Nonlocal PDEs: Analysis, Control and Beyond”, AFOSR Grant FA9550-18-1-0242.
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