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This paper studies an evacuation problem described by a leader-follower model with bounded confidence under predictive mechanisms. We design a control strategy in such a way that agents are guided by a leader, which follows the evacuation path. The proposed evacuation algorithm is based on Model Predictive Control (MPC) that uses the current and the past information of the system to predict future agents’ behaviors. It can be observed that, with MPC method, the leader-following consensus is obtained faster in comparison to the conventional optimal control technique. The effectiveness of the developed MPC evacuation algorithm with respect to different parameters and different time domains is illustrated by numerical examples.
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Tom
Strony
629--644
Opis fizyczny
Bibliogr. 25 poz., rys., wzory
Twórcy
autor
- Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
autor
- Faculty of Computer Science, Bialystok University of Technology, 15-351 Białystok, Poland
autor
- Institute of Systems and Robotics, DEEC-UC, 3030-290 Coimbra, Portugal & Department of Mathematics, University of Trás-os-Montes e Alto Douro (UTAD), 5000-801 Vila Real, Portuga
autor
- Faculty of Computer Science, Bialystok University of Technology, 15-351 Białystok, Poland
autor
- Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Bibliografia
- [1] H. Abdelgawad and B. Abdulhai: Emergency evacuation planning as a network design problem: A critical review. Transportation Letters: The International Journal of Transportation Research, 1 (2009), 41-58, DOI: 10.3328/TL.2009.01.01.41-58.
- [2] R. Alizadeh: A dynamic cellular automaton model for evacuation process with obstacles, Safety Science, 49(2), (2011), 315-323, DOI: 10.1016/j.ssci.2010.09.006.
- [3] R. Almeida, E. Girejko, L. Machado, A.B. Malinowska, and N. Martins: Application of predictive control to the Hegselmann-Krause model, Mathematical Methods in the Applied Sciences, 41(18), (2018), 9191-9202, DOI: 10.10022Fmma.5132.
- [4] B. Aulbach and S. Hilger: A unified approach to continuous and discrete dynamics, ser. Colloq. Math. Soc. Janos Bolyai, vol. 53, North-Holland, Amsterdam, 1990.
- [5] H. Bi and E. Gelenbe: A survey of algorithms and systems for evacuating people in confined spaces, Electronics, 2019 8(6), (2019), 711, DOI: 10.3390/electronics8060711.
- [6] V.D. Blondel, J.M. Hendrickx, and J.N. Tsitsiklis: On Krause’s multiagent consensus model with state-dependent connectivity, IEEE Transactions on Automatics Control, vol. 54(11), (2009), 2586-2597, DOI: 10.1109/TAC.2009.2031211.
- [7] V.D. Blondel, J.M. Hendrickx, and J.N. Tsitsiklis: Continuous-time average-preserving opinion dynamics with opinion-dependent communications, SIAM Journal on Control and Optimization, vol. 48(8), (2010), 5214-5240, DOI: 10.1137/090766188
- [8] M. Bohner and A. Peterson: Dynamic equations on time scales, Boston, MA: Birkhäuser Boston, 2001.
- [9] R.M. Colombo and M. D. Rosini: Pedestrian flows and non-classical shocks, Mathematical Methods in the Applied Sciences, 28(13), (2005), 1553-1567, DOI: 10.1002/mma.624.
- [10] E. Girejko, L. Machado, A.B. Malinowska, and N. Martins: Krause’s model of opinion dynamics on isolated time scales, Mathematical Methods in the Applied Sciences, 39 (2016), 5302-5314, DOI: 10.1002/mma.3916.
- [11] R. Hegselmann and U. Krause: Opinion dynamics and bounded confidence models, analysis, and simulation, Journal of Artificial Societies and Social Simulation, 5(3), (2002), http://jasss.soc.surrey.ac.uk/5/3/2.html.
- [12] D. Helbing and P. Molnár: Social force model for pedestrian dynamics, Physical Review E, 51(5), (1995), 4282-4286, DOI: 10.1103/PhysRevE.51.4282.
- [13] R. Hilscher and V. Zeidan: Weak maximum principle and accessory problem for control problems on time scales, Nonlinear Analysis, 70(9), (2009), 3209-3226, DOI: 10.1016/j.na.2008.04.025.
- [14] L. Huang, S.C. Wong, M. Zhang, C.-W. Shu, and W.H.K. Lam: Revisiting Hughes’ dynamics continuum model for pedestrian flow and the development of an efficient solution algorithm, Transportation Research Part B: Methodological, 43(1), (2009), 127-141, DOI: 10.1016/j.trb.2008.06.003.
- [15] R.L. Hughes: A continuum theory for the flow of pedestrians, Transportation Research Part B: Methodological, 36(6), (2002), 507-535, DOI: 10.1016/S0191-2615(01)00015-7.
- [16] R. Lohner: On the modeling of pedestrian motion, Applied Mathematical Modeling, 34(2), (2010), 366-382, DOI: 10.1016/j.apm.2009.04.017.
- [17] S.J. Qin and T.A. Badgwell: An Overview of Nonlinear Model Predictive Control Applications, Allgöwer F., Zheng A. ed., ser. Nonlinear Model Predictive Control. Progress in Systems and Control Theory. Birkhäuser, Basel, 2000, vol. 26, pp. 369-392.
- [18] S. Wojnar, T. Polóni, P. Šimončič, B. Rohal’-Ilkiv, M. Honek (and) J. Csambál: Real-time implementation of multiple model based predictive control strategy to air/fuel ratio of a gasoline engine. Archives of Control Sciences, 23(1), (2013), 93-106.
- [19] S. Daniar, M. Shiroei and R. Aazami: Multivariable predictive control considering time delay for load-frequency control in multi-area power systems. Archives of Control Sciences, 26(4), (2016), 527-549, DOI: 10.1515/acsc-2016-0029.
- [20] Y. Yang, D.V. Dimarogonas, and X. Hu: Optimal leader-follower control for crowd evacuation, Proc. 52nd IEEE Conf. Decision Control (CDC), (2013), 2769-2774, DOI: 10.1109/CDC.2013.6760302.
- [21] Z. Zainuddin and M. Shuaib: Modification of the decision-making capability in the social force model for the evacuation process, Transport Theory and Statistical Physics, 39(1), (2011), 47-70, DOI: 10.1080/ 00411450.2010.529979.
- [22] H.-T. Zhang, M.Z. Chen, G.-B. Stan, and T. Zhou: Ultrafast consensus via predictive mechanisms, Europhysics Letters, 83, (2008), no. 40003.
- [23] H.-T. Zhang, M.Z. Chen, G.-B. Stan, T. Zhou, and J.M. Maciejowski: Collective behaviour coordination with predictive mechanisms, IEEE Circuits Systems Magazine, 8, (2008) 67-85, DOI: 10.1109/MCAS.2008.928446.
- [24] L. Zhang, J. Wang, and Q. Shi: Multi-agent based modeling and simulating for evacuation process in stadium, Journal of Systems Science and Complexity, 27(3), (2014), 430-444, DOI: 10.1007/s11424-014-3029-5.
- [25] Y. Zheng, B. Jia, X.-G. Li, and N. Zhu: Evacuation dynamics with fire spreading based on cellular automaton, Physica A: Statistical Mechanics and Its Applications, 390(18-19), (2011), 3147-3156, DOI: 10.1016/j.physa.2011.04.011.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
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