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In this chapter, we discuss the mathematical modeling of egressing pedestrians in an unknown environment with multiple exits. We investigate different control problems to enhance the evacuation time of a crowd of agents, by few informed individuals, named leaders. Leaders are not recognizable as such and consist of two groups: a set of unaware leaders moving selfishly toward a fixed target, whereas the rest is coordinated to improve the evacuation time introducing different performance measures. Follower-leader dynamics is initially described microscopically by an agent-based model, subsequently a mean-field type model is introduced to approximate the large crowd of followers. The mesoscopic scale is efficiently solved by a class of numerical schemes based on direct simulation Monte-Carlo methods. Optimization of leader strategies is performed by a modified compass search method in the spirit of metaheuristic approaches. Finally, several virtual experiments are studied for various control settings and environments.
Navigation tasks often cannot be defined in terms of a target, either because global position information is unavailable or unreliable or because target location is not explicitly known a priori. This task is then often defined indirectly as a source
Two major problems in modern cities are air contamination and road congestion. They are closely related and present a similar origin: traffic flow. To face these problems, local governments impose traffic restrictions to prevent the entry of vehicles
In an emergency situation, imitation of strategies of neighbours can lead to an order-disorder phase transition, where spatial clusters of pedestrians adopt the same strategy. We assume that there are two strategies, cooperating and competitive, whic
Statistical analysis of massive datasets very often implies expensive linear algebra operations with large dense matrices. Typical tasks are an estimation of unknown parameters of the underlying statistical model and prediction of missing values. We
Policy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case. Here we ana