A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 3 Issue 3
Jul.  2016

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 7.847, Top 10% (SCI Q1)
    CiteScore: 13.0, Top 5% (Q1)
    Google Scholar h5-index: 64, TOP 7
Turn off MathJax
Article Contents
Kecai Cao, YangQuan Chen and Daniel Stuart, "A Fractional Micro-Macro Model for Crowds of Pedestrians Based on Fractional Mean Field Games," IEEE/CAA J. of Autom. Sinica, vol. 3, no. 3, pp. 261-270, 2016.
Citation: Kecai Cao, YangQuan Chen and Daniel Stuart, "A Fractional Micro-Macro Model for Crowds of Pedestrians Based on Fractional Mean Field Games," IEEE/CAA J. of Autom. Sinica, vol. 3, no. 3, pp. 261-270, 2016.

A Fractional Micro-Macro Model for Crowds of Pedestrians Based on Fractional Mean Field Games

Funds:

This work was supported by National Natural Science Foundation of China (61374055), Natural Science Foundation of Jiangsu Province (BK20131381), China Postdoctoral Science Foundation funded project (2013M541663), Jiangsu Planned Projects for Postdoctoral Research Funds (1202015C), Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry (BJ213022), Scientific Research Foundation of Nanjing University of Posts and Telecommunications (NY214075, XJKY14004).

  • Modeling a crowd of pedestrians has been considered in this paper from different aspects. Based on fractional microscopic model that may be much more close to reality, a fractional macroscopic model has been proposed using conservation law of mass. Then in order to characterize the competitive and cooperative interactions among pedestrians, fractional mean field games are utilized in the modeling problem when the number of pedestrians goes to infinity and fractional dynamic model composed of fractional backward and fractional forward equations are constructed in macro scale. Fractional micromacro model for crowds of pedestrians are obtained in the end. Simulation results are also included to illustrate the proposed fractional microscopic model and fractional macroscopic model, respectively.

     

  • loading
  • [1]
    West B J, Turalska M, Grigolini P. Networks of Echoes: Imitation, Innovation and Invisible Leaders. Switzerland: Springer International Publishing, 2014.
    [2]
    Helbing D, Molnar P. Social force model for pedestrian dynamics. Physical Review E, 1995, 51(5): 4282-4286
    [3]
    Helbing D, Farkas I, Vicsek T. Simulating dynamical features of escape panic. Nature, 2000, 407(6803): 487-490
    [4]
    Bellomo N, Bianca C, Coscia V. On the modeling of crowd dynamics: an overview and research perspectives. SeMA Journal, 2011, 54(1): 25-46
    [5]
    Couzin I D, Krause J, Franks N R, Levin S A. Effective leadership and decision-making in animal groups on the move. Nature, 2005, 433(7025): 513-516
    [6]
    Couzin I D. Collective cognition in animal groups. Trends in Cognitive Sciences, 2009, 13(1): 36-43
    [7]
    Song W G, Xu X, Wang B H, Ni S J. Simulation of evacuation processes using a multi-grid model for pedestrian dynamics. Physica A, 2006, 363(2): 492-500
    [8]
    Shiwakoti N, Sarvi M, Rose G, Burd M. Animal dynamics based approach for modeling pedestrian crowd egress under panic conditions. Transportation Research, Part B: Methodological, 2011, 45(9): 1433-1449
    [9]
    Kachroo P. Pedestrian Dynamics: Mathematical Theory and Evacuation Control. Boca Raton: CRC Press, 2009.
    [10]
    Helbing D. A fluid dynamic model for the movement of pedestrians. Complex Systems, 1992, 6: 391-415
    [11]
    Hughes R L. A continuum theory for the flow of pedestrians. Transportation Research, Part B: Methodological, 2002, 36(6): 507-535
    [12]
    Hughes R L. The flow of human crowds. Annual Review of Fluid Mechanics, 2003, 35: 169-182
    [13]
    Jiang Y Q, Zhang P, Wong S C, Liu R X. A higher-order macroscopic model for pedestrian flows. Physica A: Statistical Mechanics and its Applications, 2010, 389(21): 4623-4635
    [14]
    Al-nasur S J. New Models for Crowd Dynamics and Control [Ph. D. dissertation], Virginia Polytechnic Institute and State University, Virginia, 2006.
    [15]
    Lattanzio C, Maurizi A, Piccoli B. Moving bottlenecks in car traffic flow: a PDE-ODE coupled model. SIAM Journal on Mathematical Analysis, 2011, 43(1): 50-67
    [16]
    Ishiwata R, Sugiyama Y. Relationships between power-law longrange interactions and fractional mechanics. Physica A, 2012, 391(23): 5827-5838
    [17]
    Achdou Y, Camilli F, Capuzzo-Dolcetta I. Mean field games: numerical methods for the planning problem. SIAM Journal on Control and Optimization, 2012, 50(1): 77-109
    [18]
    Caines P E. Mean field stochastic control. In: Proceedings of the 48th Conference on Decision and Control and the 28th Chinese Control Conference. Shanghai, China: IEEE, 2009.
    [19]
    Gueant. A reference case for mean field games models. Journal de Mathematiques Pures et Appliquees, 2009, 92(3): 276-294
    [20]
    Dogbe C. Modeling crowd dynamics by the mean-field limit approach. Mathematical and Computer Modelling, 2010, 52(9-10): 1506-1520
    [21]
    Nourian M, Malhame R P, Huang M Y, Caines P E. Mean field (NCE) formulation of estimation based leader-follower collective dynamics. International Journal of Robotics & Automation, 2011, 26(1): 120-129
    [22]
    Nourian M, Caines P E, Malhame R P, Huang M Y. Mean field LQG control in leader-follower stochastic multi-agent systems: likelihood ratio based adaptation. IEEE Transactions on Automatic Control, 2012, 57(11): 2801-2816
    [23]
    Nourian M, Caines P E, Malhame R P, Huang M Y. Nash, social and centralized solutions to consensus problems via mean field control theory. IEEE Transactions on Automatic Control, 2013, 58(3): 639-653
    [24]
    Lachapelle A, Wolfram M T. On a mean field game approach modeling congestion and aversion in pedestrian crowds. Transportation Research, Part B: Methodological, 2011, 45(10): 1572-1589
    [25]
    Chevalier G, Le Ny J, Malhame R. A micro-macro traffic model based on mean-field games. In: Proceedings of the 2015 American Control Conference. Chicago, IL, USA: IEEE, 2015. 1983-1988
    [26]
    Bogdan P, Marculescu R. A fractional calculus approach to modeling fractal dynamic games. In: Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference. Orlando, FL: IEEE, 2011. 255-260
    [27]
    Cao K C, Zeng C B, Stuart D, Chen Y Q. Fractional order dynamic modeling of crowd pedestrians. In: Proceedings of the 5th Symposium on Fractional Differentiation and its Applications. 2012.
    [28]
    Cao K C, Chen Z Q, Stuart D, Yue D. Cyber-physical modeling and control of crowd of pedestrians: a review and new framework. IEEE/CAA Journal of Automatica Sinica, 2015, 2(3): 334-344
    [29]
    Cao K C, Chen Y Q, Stuart D. A new fractional order dynamic model for human crowd stampede system. In: Proceedings of the ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Boston, USA: ASME, 2015.
    [30]
    Parvate A, Gangal A D. Fractal differential equations and fractal-time dynamical systems. Pramana, 2005, 64(3): 389-409
    [31]
    Das S. Functional Fractional Calculus. Berlin Heidelberg: Springer-Verlag, 2011.
    [32]
    Wang L F, Yang X J, Baleanu D, Cattani C, Zhao Y. Fractal dynamical model of vehicular traffic flow within the local fractional conservation laws. Abstract and Applied Analysis, 2014, 2014(2014): Article ID 635760
    [33]
    Kachroo P, Al-Nasur S J, Wadoo S A, Shende A. Pedestrian Dynamics: Feedback Control of Crowd Evacuation. Berlin Heidelberg: Springer-Verlag, 2008.

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1115) PDF downloads(4) Cited by()

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return