TY - GEN
T1 - Sparse control to prevent Black Swan clustering in collective dynamics
AU - Piccoli, Benedetto
AU - Duteil, Nastassia Pouradier
AU - Trélat, Emmanuel
N1 - Publisher Copyright:
© 2018 AACC.
PY - 2018/8/9
Y1 - 2018/8/9
N2 - In this paper, we elaborate control strategies to prevent clustering effects, as opposed to numerous works in the literature seeking to control multi-agent systems to achieve consensus. We consider general controlled collective dynamics and show how the group variance should be replaced by an entropy-type functional to measure clustering. Then we focus on Hegselmann-Krause type models and propose sparse declustering controls for the discrete system as well as for its mean-field limit. The behavior or the interaction function at zero and at infinity characterizes whether clustering can be avoided by controlling the system. Such results include the description of black holes (where complete collapse to consensus is not avoidable), safety regions (where the control can keep the system far from clustering), basins of attraction (attractive zones around the clustering manifold) and collapse prevention.
AB - In this paper, we elaborate control strategies to prevent clustering effects, as opposed to numerous works in the literature seeking to control multi-agent systems to achieve consensus. We consider general controlled collective dynamics and show how the group variance should be replaced by an entropy-type functional to measure clustering. Then we focus on Hegselmann-Krause type models and propose sparse declustering controls for the discrete system as well as for its mean-field limit. The behavior or the interaction function at zero and at infinity characterizes whether clustering can be avoided by controlling the system. Such results include the description of black holes (where complete collapse to consensus is not avoidable), safety regions (where the control can keep the system far from clustering), basins of attraction (attractive zones around the clustering manifold) and collapse prevention.
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U2 - 10.23919/ACC.2018.8430970
DO - 10.23919/ACC.2018.8430970
M3 - Conference contribution
AN - SCOPUS:85052557087
SN - 9781538654286
T3 - Proceedings of the American Control Conference
SP - 955
EP - 960
BT - 2018 Annual American Control Conference, ACC 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 Annual American Control Conference, ACC 2018
Y2 - 27 June 2018 through 29 June 2018
ER -