Abstract
This paper pertains to the study of finite-time control of one dimensional crowd evacuation system. Benefiting from the research of fluid dynamics and vehicle traffic, a one dimensional crowd evacuation system is constructed, whose density-velocity relationship is represented by a diffusion model. In order to deal with the nondirectionality of crowd movement, the free flow speed is chosen as a control variable. Since the control variable is included in a partial derivative, it increases the difficulty of designing the controller. In this paper, finite-time controller is designed, which not only guarantees the effective evacuation, but also obtains the estimation of evacuation time. Then, finite-time tracking problem is solved, which makes the density converge to a given density. Finally, numerical examples illustrate the effectiveness of the controllers.
Highlights
In everyday life, crowds would gather in many places, for example, subway stations, stadiums, and cinemas
Modeling the crowd dynamics is the primary task of crowd evacuation, but due to the complexity and uncertainty of crowd dynamics, it is very difficult to build a model that suits all situations
The Lighthill-Whitham-Richards (LWR) model [27, 28] based on the conservation law of mass is recommended in this paper to represent the crowd evacuation dynamics in one dimension, implying that the number of pedestrians coming in and going out of a corridor section account for the change of crowd density on that section
Summary
Crowds would gather in many places, for example, subway stations, stadiums, and cinemas. A first-order continuum model was developed to describe the pedestrian dynamics in [10]. All above focus on modeling the pedestrian dynamics in different situations, but few literatures present strategies for controlling the crowd dynamics. The problem of finite-time evacuation is studied. Benefiting from Orlov’s research [19], finite-time controller is designed to evacuate pedestrians in finite time, and the finite-time control method is extended to deal with the tracking problem which makes the crowd density follow a given reference density.
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