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Invisible control of self-organizing agents leaving unknown environments

Albi, Giacomo; Bongini, Mattia; Cristiani, Emiliano; Kalise, Dante

Authors

Giacomo Albi

Mattia Bongini

Emiliano Cristiani



Abstract

© 2016 Society for Industrial and Applied Mathematics. In this paper we are concerned with multiscale modeling, control, and simulation of self-organizing agents leaving an unknown area under limited visibility, with special emphasis on crowds. We first introduce a new microscopic model characterized by an exploration phase and an evacuation phase. The main ingredients of the model are an alignment term, accounting for the herding effect typical of uncertain behavior, and a random walk, accounting for the need to explore the environment under limited visibility. We consider both metrical and topological interactions. Moreover, a few special agents, the leaders, not recognized as such by the crowd, are "hidden" in the crowd with a special controlled dynamic. Next, relying on a Boltzmann approach, we derive a mesoscopic model for a continuum density of followers, coupled with a microscopic description for the leaders' dynamics. Finally, optimal control of the crowd is studied. It is assumed that leaders aim at steering the crowd towards the exits so to ease the evacuation and limit clogging effects, and locally optimal behavior of leaders is computed. Numerical simulations show the efficiency of the control techniques in both microscopic and mesoscopic settings. We also perform a real experiment with people to study the feasibility of such a bottom-up control technique.

Journal Article Type Article
Publication Date Aug 30, 2016
Journal SIAM Journal on Applied Mathematics
Print ISSN 0036-1399
Electronic ISSN 1095-712X
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 76
Issue 4
Pages 1683-1710
APA6 Citation Albi, G., Bongini, M., Cristiani, E., & Kalise, D. (2016). Invisible control of self-organizing agents leaving unknown environments. SIAM Journal on Applied Mathematics, 76(4), 1683-1710. https://doi.org/10.1137/15M1017016
DOI https://doi.org/10.1137/15M1017016
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