Multi-agent stabilisation of the psychological dynamics of one-dimensional crowds

This work is part of an investigation aimed at applying the tools of control theory to gain a deeper understanding of the behaviour and attitudes that develop in individuals and in groups of people, with the goal of ultimately controlling the relevant psychological dynamics. The present treatment investigates an approach to stabilise one-dimensional crowds, that is, structures where people are aligned in a queue. The psychological dynamics considered here are based on the notion of suggestibility put forth by Gustave Le Bon. Control action is carried out by certain authoritative figures, termed control agents, who are interspersed throughout the crowd in some predetermined arrangement, subject to one control agent being positioned at one end of the queue. The main result of this paper is the existence of a state-feedback control law for each control agent that, possibly with some communication among control agents, stabilises the crowd. Advantages of employing multiple control agents instead of a single control agent are highlighted, and, throughout, the main stabilisation results are verified using simulations. Finally, the possibility of extending the control strategy to two-dimensional crowds is briefly explored.