D. Ruiz-Balet, E. Zuazua 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 (2019), pp. 343-363. DOI: 10.1007/978-3-030-29951-4_15
Abstract: We analyze the problem of controlling to consensus a nonlinear system modeling opinion spreading. Our strategy makes use of known results on the controllability of spatially discretized semilinear parabolic equations. Both systems can be linked through time-rescaling. This allows us to derive explicit exponential estimates on the cost of approximately controlling these systems to consensus, as a function of the number of agents N entering in the system and the control time-horizon T.