Abstract
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.
This paper is dedicated to Jüri Engelbrecht with gratitude and admiration
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Acknowledgements
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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Ruiz-Balet, D., Zuazua, E. (2019). A Parabolic Approach to the Control of Opinion Spreading. In: Berezovski, A., Soomere, T. (eds) Applied Wave Mathematics II. Mathematics of Planet Earth, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-030-29951-4_15
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