Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2013, Article ID 783279, 9 pages
http://dx.doi.org/10.1155/2013/783279
Research Article

Cucker-Smale Flocking with Bounded Cohesive and Repulsive Forces

1School of Electronics and Information, Hangzhou Dianzi University, Hangzhou 310018, China
2School of Information Engineering, Huanghuai University, Henan 463000, China
3Department of Mathematics, Southeast University, Nanjing 210096, China
4Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
5School of Science, Linyi University, Linyi, Shandong 276005, China

Received 6 July 2013; Accepted 27 August 2013

Academic Editor: A. M. Elaiw

Copyright © 2013 Qiang Song et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. W. Reynolds, “Flocks, herds, and schools: a distributed behavioral model,” Computer Graphics, vol. 21, no. 4, pp. 25–34, 1987. View at Google Scholar · View at Scopus
  2. T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, and O. Shochet, “Novel type of phase transition in a system of self-driven particles,” Physical Review Letters, vol. 75, no. 6, pp. 1226–1229, 1995. View at Publisher · View at Google Scholar · View at Scopus
  3. A. Jadbabaie, J. Lin, and A. S. Morse, “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 988–1001, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  4. R. Olfati-Saber, “Flocking for multi-agent dynamic systems: algorithms and theory,” IEEE Transactions on Automatic Control, vol. 51, no. 3, pp. 401–420, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  5. H. G. Tanner, A. Jadbabaie, and G. J. Pappas, “Flocking in fixed and switching networks,” IEEE Transactions on Automatic Control, vol. 52, no. 5, pp. 863–868, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  6. D. Gu and Z. Wang, “Leader-follower flocking: algorithms and experiments,” IEEE Transactions on Control Systems Technology, vol. 17, no. 5, pp. 1211–1219, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. H. Su, X. Wang, and G. Chen, “A connectivity-preserving flocking algorithm for multi-agent systems based only on position measurements,” International Journal of Control, vol. 82, no. 7, pp. 1334–1343, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  8. J. Zhou, X. Wu, W. Yu, M. Small, and J. Lu, “Flocking of multi-agent dynamical systems based on pseudo-leader mechanism,” Systems & Control Letters, vol. 61, no. 1, pp. 195–202, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  9. G. Wen, Z. Duan, H. Su, G. Chen, and W. Yu, “A connectivity-preserving flocking algorithm for multi-agent dynamical systems with bounded potential function,” IET Control Theory & Applications, vol. 6, no. 6, pp. 813–821, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  10. J. Zhu, J. Lü, and X. Yu, “Flocking of multi-agent non-holonomic systems with proximity graphs,” IEEE Transactions on Circuits and Systems I, vol. 60, no. 1, pp. 199–210, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  11. F. Cucker and S. Smale, “Emergent behavior in flocks,” IEEE Transactions on Automatic Control, vol. 52, no. 5, pp. 852–862, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  12. J. Shen, “Cucker-Smale flocking under hierarchical leadership,” SIAM Journal on Applied Mathematics, vol. 68, no. 3, pp. 694–719, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  13. S. Y. Ha and J. G. Liu, “A simple proof of the Cucker-Smale flocking dynamics and mean-field limit,” Communications in Mathematical Sciences, vol. 7, no. 2, pp. 297–325, 2009. View at Google Scholar · View at MathSciNet
  14. S. Y. Ha, T. Ha, and J. H. Kim, “Emergent behavior of a Cucker-Smale type particle model with nonlinear velocity couplings,” IEEE Transactions on Automatic Control, vol. 55, no. 7, pp. 1679–1683, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  15. J. Park, H. J. Kim, and S. Y. Ha, “Cucker-Smale flocking with inter-particle bonding forces,” IEEE Transactions on Automatic Control, vol. 55, no. 11, pp. 2617–2623, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  16. L. Perea, G. Gómez, and P. Elosegui, “Extension of the Cucker-Smale control law to space flight formations,” Journal of Guidance, Control, and Dynamics, vol. 32, no. 2, pp. 526–536, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. F. Cucker and J. G. Dong, “Avoiding collisions in flocks,” IEEE Transactions on Automatic Control, vol. 55, no. 5, pp. 1238–1243, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  18. V. Gazi and K. M. Passino, “Stability analysis of swarms,” IEEE Transactions on Automatic Control, vol. 48, no. 4, pp. 692–697, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  19. V. Gazi and K. M. Passino, “A class of attractions/repulsion functions for stable swarm aggregations,” International Journal of Control, vol. 77, no. 18, pp. 1567–1579, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  20. H. K. Khalil, Nonlinear Systems, Prentice Hall, Englewood Cliffs, NJ, USA, 3rd edition, 2002.