Sliding Mode Control of Crowd Dynamics

Journal of Advanced Transportation

Cui

Jiang

2019

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.

“…Substituting the distributed controller (25) into (27) for ≥ 0, and using the Leibniz integral rule (15), one can derivė…”

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite-Time Control of One Dimensional Crowd Evacuation System

Journal of Advanced Transportation

Cui

Jiang

2019

“…where is the control gains of the link flow control model. Substituting (27) into (29), we can obtain the following equations: At present, in (30), all variables except the walking speed V are known. The variables in and out can be produced by the NFCM and the section densities can be observed and analyzed by the sensors.…”

Section: Link Flow Control Modelmentioning

confidence: 99%

“…The feedback control models have been proposed to support the smooth evacuation in rooms [24,25], corridors [26], and networks [27] based on the linear or nonlinear ordinary differential equation model (ODE) and hyperbolic partial differential equations (PDEs). Sliding mode control is also used to control the crowd evacuation [28] and avoid the congestion in bottleneck of corridors [29] based on PDEs.…”

Section: Introductionmentioning

confidence: 99%

Level-of-Service Based Hierarchical Feedback Control Method of Network-Wide Pedestrian Flow

Zhang

Jia

Mathematical Problems in Engineering

2016

Pedestrian flow control is usually used to manage the crowd motion in public facilities to avoid congestion. We propose a network-wide pedestrian flow model based on the modified cell transmission model which describes the link flow as ordinary differential equations. The network flow control model (NFCM) is proposed to limit the number of pedestrians in a network according to the level-of-service requirements; however, the NFCM cannot ensure the uniform link density which is a premise of using NFCM. As a solution, the link flow control model (LFCM) is proposed to adjust the walking speed of pedestrians to realize the uniform link density. The NFCM provides the inputs for the LFCM and the LFCM compensates the deficiency of NFCM. Both NFCM and LFCM control the pedestrian flow in a cooperative way, and thus they form the hierarchical feedback control model (HFCM) of network-wide pedestrian flow. At last, the proposed HFCM is applied to control the crowd of a hall and the comparison of the simulation results in the controlled and uncontrolled scenarios shows that the proposed HFCM has the capability to suggest the optimal link inflows and walking speeds in real time to meet the LOS requirement.

“…The dynamic of two intersecting pedestrian flows was modelled in [12] by using nonlinear partial differential equation, and then was illustrated with macroscopic and microscopic simulations. Wadoo [13], [14] used a vehicle traffic model to describe the pedestrian dynamics, and chose the free flow speed as the control variable to solve the problem of the multidirectionality of the pedestrian movement. Qin et al integrated the Lighthill-Whitham-Richards(LWR) model [15], [16] and the diffusion model to describe crowd dynamics, and designed boundary controller [17] and finite time controller [18], respectively.…”

Section: Introductionmentioning

confidence: 99%

Unit Sliding Mode Control for Disturbed Crowd Dynamics System Based on Integral Barrier Lyapunov Function

2020

IEEE Access

This paper presents a new tracking controller for a crowd dynamics system. The crowd dynamics are described by a continuum model in the macro-scale. An appropriate control variable is chosen to solve the problem of the multi-directionality of crowd movement. In order to stabilize the state density of the disturbed crowd dynamics system at a given reference density, a unit sliding mode controller based on the integral barrier Lyapunov function is designed, and the reaching law approach is used to avoid chattering. By ensuring the boundedness of the integral barrier Lyapunov function in the closed-loop, the global constraints of the system state variables are obtained. The design of the controller and the stability analysis of the closed-loop system are all done in the distributed parameter system. A numerical example illustrates the utility of the proposed controller. INDEX TERMS Integral barrier Lyapunov function, unit sliding mode control, tracking control, disturbed crowd dynamics system, distributed parameter system.