On Collision Avoiding Fixed-Time Flocking with Measurable Diameter to a Cucker–Smale-Type Self-Propelled Particle Model
Dealing with the fixed-time flocking issue is one of the most challenging problems for a Cucker–Smale-type self-propelled particle model. In this article, the fixed-time flocking is established by employing a fixed-time stability theorem when the communication weight function has a positive infimum....
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| Published in | Complexity (New York, N.Y.) Vol. 2020; no. 2020; pp. 1 - 12 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Cairo, Egypt
Hindawi Publishing Corporation
2020
Hindawi John Wiley & Sons, Inc Hindawi Limited Hindawi-Wiley |
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| Abstract | Dealing with the fixed-time flocking issue is one of the most challenging problems for a Cucker–Smale-type self-propelled particle model. In this article, the fixed-time flocking is established by employing a fixed-time stability theorem when the communication weight function has a positive infimum. Compared with the initial condition-based finite-time stability, an upper bound of the settling time in this paper is merely dependent on the design parameters. Moreover, the size of the final flocking can be estimated by the number of particles and the initial states of the system. In addition, a sufficient condition is formulated to guarantee that all particles do not collide during the process of the flocking. These results can give a reasonable explanation to some flocking phenomena such as bird flocks, fish schools, or human group behaviors. Finally, three numerical examples are granted to display the performance of the obtained results. |
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| AbstractList | Dealing with the fixed-time flocking issue is one of the most challenging problems for a Cucker–Smale-type self-propelled particle model. In this article, the fixed-time flocking is established by employing a fixed-time stability theorem when the communication weight function has a positive infimum. Compared with the initial condition-based finite-time stability, an upper bound of the settling time in this paper is merely dependent on the design parameters. Moreover, the size of the final flocking can be estimated by the number of particles and the initial states of the system. In addition, a sufficient condition is formulated to guarantee that all particles do not collide during the process of the flocking. These results can give a reasonable explanation to some flocking phenomena such as bird flocks, fish schools, or human group behaviors. Finally, three numerical examples are granted to display the performance of the obtained results. |
| Audience | Academic |
| Author | Xiao, Qizhen Xu, Zhenghua Ouyang, Zigen Liu, Hongliang |
| Author_xml | – sequence: 1 fullname: Ouyang, Zigen – sequence: 2 fullname: Xu, Zhenghua – sequence: 3 fullname: Liu, Hongliang – sequence: 4 fullname: Xiao, Qizhen |
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| Cites_doi | 10.1137/090757290 10.1016/j.automatica.2014.08.028 10.1016/j.nonrwa.2008.08.010 10.1080/00207179.2012.717722 10.1142/s0218202510004684 10.1002/cplx.21747 10.1109/tcyb.2015.2477366 10.1137/060673254 10.1002/rnc.3498 10.1016/j.sysconle.2016.03.006 10.1016/j.automatica.2006.06.015 10.1016/j.aml.2018.06.018 10.1109/tcsi.2012.2190676 10.4310/cms.2009.v7.n2.a9 10.1137/060675861 10.1016/j.aml.2019.07.004 10.1109/tcst.2009.2016428 10.1109/tcyb.2016.2556002 10.1016/j.neucom.2014.12.033 10.1049/iet-cta.2014.1301 10.1016/j.cnsns.2019.04.006 10.1109/tac.2007.895842 10.4310/cms.2012.v10.n2.a10 10.1109/tnnls.2015.2425933 10.1016/j.automatica.2013.08.003 10.1016/j.jmaa.2014.01.036 10.1016/j.amc.2015.08.048 10.1016/j.automatica.2011.08.042 10.1016/j.jmaa.2018.04.070 10.1080/00207179.2017.1313453 10.4134/bkms.b150629 10.1016/j.jfranklin.2018.04.026 10.1109/tac.2011.2107113 10.1137/0324047 10.1137/s0363012997321358 10.1080/00207721.2014.925608 10.1109/tac.2011.2179869 10.1016/j.neunet.2017.02.001 10.1016/j.cnsns.2018.10.017 10.1049/iet-cta.2017.1094 10.1049/iet-cta.2014.0995 10.1016/j.automatica.2015.01.021 |
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| Copyright | Copyright © 2020 Qizhen Xiao et al. COPYRIGHT 2020 John Wiley & Sons, Inc. Copyright © 2020 Qizhen Xiao et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. http://creativecommons.org/licenses/by/4.0 |
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| SubjectTerms | Animal behavior Birds Collision avoidance Communication Comparative analysis Design parameters Diameters Inequality Infimum Stability Upper bounds Weighting functions |
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| Title | On Collision Avoiding Fixed-Time Flocking with Measurable Diameter to a Cucker–Smale-Type Self-Propelled Particle Model |
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