Sparse control of Hegselmann-Krause models: Black hole and declustering
| Autor: | Emmanuel Trélat, Nastassia Pouradier Duteil, Benedetto Piccoli |
|---|---|
| Přispěvatelé: | Department of Mathematical Sciences [Camden], Rutgers University [Camden], Rutgers University System (Rutgers)-Rutgers University System (Rutgers), Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Control And GEometry (CaGE ) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
0209 industrial biotechnology
Collective behavior Mathematical optimization Control and Optimization 02 engineering and technology 01 natural sciences Active particles Black swan Set (abstract data type) 020901 industrial engineering & automation Convergence (routing) Control FOS: Mathematics 0101 mathematics [MATH]Mathematics [math] Cluster analysis Mathematics - Optimization and Control Declustering Mathematics Applied Mathematics 010102 general mathematics Function (mathematics) Variance (accounting) Kinetic model Optimization and Control (math.OC) Pairwise comparison AMS Subject Classifications: 93C15 93C20 91D10 35B36 34H05 [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Focus (optics) |
| Zdroj: | SIAM Journal on Control and Optimization SIAM Journal on Control and Optimization, 2019, 57 (4), pp.2628--2659. ⟨10.1137/18M1168911⟩ SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2019, 57 (4), pp.2628--2659. ⟨10.1137/18M1168911⟩ |
| ISSN: | 0363-0129 1095-7138 |
| DOI: | 10.1137/18M1168911⟩ |
| Popis: | International audience; This paper elaborates control strategies to prevent clustering effects in opinion formation models. This is the exact opposite of numerous situations encountered in the literature where, on the contrary, one seeks controls promoting consensus. In order to promote declustering, instead of using the classical variance that does not capture well the phenomenon of dispersion, we introduce an entropy-type functional that is adapted to measuring pairwise distances between agents. We then focus on a Hegselmann-Krause-type system and design declustering sparse controls both in finite-dimensional and kinetic models. We provide general conditions characterizing whether clustering can be avoided as function of the initial data. Such results include the description of black holes (where complete collapse to consensus is not avoidable), safety zones (where the control can keep the system far from clustering), basins of attraction (attractive zones around the clustering set) and collapse prevention (when convergence to the clustering set can be avoided). |
| Databáze: | OpenAIRE |
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