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This paper elaborates control strategies to prevent clustering effects inopinion formation models. This is the exact opposite of numerous situationsencountered in the literature where, on the contrary, one seeks controlspromoting consensus. In order to promote declustering, instead of using theclassical variance that does not capture well the phenomenon of dispersion, weintroduce an entropy-type functional that is adapted to measuring pairwisedistances between agents. We then focus on a Hegselmann-Krause-type system anddesign declustering sparse controls both in finite-dimensional and kineticmodels. We provide general conditions characterizing whether clustering can beavoided as function of the initial data. Such results include the descriptionof black holes (where complete collapse to consensus is not avoidable), safetyzones (where the control can keep the system far from clustering), basins ofattraction (attractive zones around the clustering set) and collapse prevention(when convergence to the clustering set can be avoided).

Sparse control of Hegselmann-Krause models: Black hole and declustering