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Crowds: models and control

3-7 Jun 2019
CIRM Marseille - Marseille (France)

The problem of modeling crowds of a large number of interacting agents has been an extremely challenging problem for the mathematical community. This led to the development of several key mathematical theories, catching different aspects of crowds, ranging from mean-field limits for interacting particles, to hyperbolic systems for road traffic models, to dynamics on graphs and networks, to stochastic models, and to adapted numerical methods. The conference aims to gather together different communities working on two connected problems for crowds. On one side, modeling crowds keeps being a stimulating issue, in particular for understanding the phenomenon of self-organization: how can a set of simple one-to-one interactions between agents produce macroscopic patterns, such as lines, swarms and flocks? Several mathematical communities have proposed different tools for modeling crowds, such as microscopic and macroscopic models, stochastic approaches, mean-field games or conservation laws. On the other side, the control of crowds is of paramount interest: how can an external control enforce a desired behavior to the crowd? In particular, how to drive a crowd towards an efficient macroscopic pattern, such as lines for egress problems? The control community has proposed a large spectrum of methods, such as control on graphs, numerical methods for optimization of conservation laws, control of the continuity equation. The two aspects of proper modeling and efficient control are then intimately connected. For this reason, the conference aims to strengthen connections between researchers in modeling and control of crowds.
Scientific domain : Mathematics - Analysis of PDEs - Dynamical Systems - Optimization and Control - Adaptation and Self-Organizing Systems - Chaotic Dynamics - Automatic

Place of the conference
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