Feedback Control of Crowd Evacuation in One Dimension

This paper presents a probabilistic model validation methodology for nonlinear systems in time-domain. The proposed formulation is simple, intuitive, and accounts both deterministic and stochastic nonlinear systems with parametric and nonparametric uncertainties. Instead of hard invalidation methods available in the literature, a relaxed notion of validation in probability is introduced. To guarantee provably correct inference, algorithm for constructing probabilistically robust validation certificate is given along with computational complexities. Several examples are worked out to illustrate its use. , . . . , b s ; x) stands for generalized hypergeometric function. The symbols N (., .), U (.), and A (.) are used for normal, uniform and arcsine distributions, respectively. We use the notation ξ 0 (.) to denote the joint PDF over initial states and parameters. ξ (., t) and ξ (., t) denote joint PDFs over instantaneous states and parameters, for the true and model dynamics, respectively. Similarly, η (., t) and η (., t), respectively denote joint PDFs over output spaces y and y at time t, for the true and model dynamics. The symbol x is used to denote the extended state vector obtained by augmenting the state (x) and parameter (p) vectors. We use χ to denote indicator function and # to denote cardinality. Unless stated otherwise, δ (.) stands for Dirac delta. The symbol I denotes the -by-identity

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“…Taking the outputs identical to states, the asymptotic Wasserstein distance between (33) and (35), becomes…”

Section: Example 3 Discrete-time Deterministic Dynamicsmentioning

confidence: 99%

Probabilistic model validation for uncertain nonlinear systems

Halder

Bhattacharya

2014

Automatica

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“…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

Qin

2020

IEEE Access

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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.

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“…Wadoo [15] designed advective, diffusive, and advectivediffusive controllers for crowd dynamics in one dimension. Sliding mode control method was applied to crowd dynamic models for the synthesis of robust controllers in [16]. Dong et al [17] designed feedback control law for two dimensional crowd model.…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Control of One Dimensional Crowd Evacuation System

Qin

Cui

Jiang

2019

Journal of Advanced Transportation

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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.

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Feedback Control of Crowd Evacuation in One Dimension

Cited by 38 publications

References 17 publications

Probabilistic model validation for uncertain nonlinear systems

Probabilistic model validation for uncertain nonlinear systems

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

Finite-Time Control of One Dimensional Crowd Evacuation System

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