SYMMETRY AND STABILITY OF HOMOGENEOUS FLOCKS

J. J. P. Veerman

2011

Abstract

The study of the movement of flocks, whether biological or technological, is motivated by the desire to understand the capability of coherent motion of a large number of agents that only receive very limited information. In a biological flock a large group of animals seek their course while moving in a more or less fixed formation. It seems reasonable that the immediate course is determined by leaders at the boundary of the flock. The others follow: what is their algorithm? The most popular technological application consists of cars on a one-lane road. The light turns green and the lead car accelerates. What is the efficient algorithm for the others to closely follow without accidents? In this position paper we present some general questions from a more fundamental point of view. We believe that the time is right to solve many of these questions: they are within our reach.

References

  1. Barooah, P. and Hespanha, J. P. (2005). Error amplification and disturbance propagation in vehicle strings with decentralized linear control. In IEEE conference on decision and control, volume 5, pages 4964-4969.
  2. Barooah, P. and Hespanha, J. P. (2005). Error amplification and disturbance propagation in vehicle strings with decentralized linear control. In IEEE conference on decision and control, volume 5, pages 4964-4969.
  3. Chandler, R. E., Herman, R., and Montroll, E. W. (1958). Traffic dynamics: Studies in car following. Op. Res., 6:165-184.
  4. Chandler, R. E., Herman, R., and Montroll, E. W. (1958). Traffic dynamics: Studies in car following. Op. Res., 6:165-184.
  5. Chu, K.-C. (1974). Decentralized control of high-speed vehicle strings. Transportation Science, 8(4):361-384.
  6. Chu, K.-C. (1974). Decentralized control of high-speed vehicle strings. Transportation Science, 8(4):361-384.
  7. DaFonseca, C. M. and Veerman, J. J. P. (2009). On the spectra of certain directed paths. Appl. Math. Lett., 9:1351-1355.
  8. DaFonseca, C. M. and Veerman, J. J. P. (2009). On the spectra of certain directed paths. Appl. Math. Lett., 9:1351-1355.
  9. Herman, R., Montroll, E. W., Potts, R. B., and Rothery, R. W. (1959). Traffic dynamics: Analysis and stability in car following. Op. Res., 7:86-106.
  10. Herman, R., Montroll, E. W., Potts, R. B., and Rothery, R. W. (1959). Traffic dynamics: Analysis and stability in car following. Op. Res., 7:86-106.
  11. Pant, A., Seiler, P., and Hedrick, K. (2002). Mesh stability of look-ahead systems. IEEE Trans Aut. Contr., 47(2):403-408.
  12. Pant, A., Seiler, P., and Hedrick, K. (2002). Mesh stability of look-ahead systems. IEEE Trans Aut. Contr., 47(2):403-408.
  13. Sullivan, W. (2010). Boundary Conditions and a One Lane Linear model of Traffic Flow. Portland State University, Master's Thesis.
  14. Sullivan, W. (2010). Boundary Conditions and a One Lane Linear model of Traffic Flow. Portland State University, Master's Thesis.
  15. Swaroop, D. and Hedrick, K. (1996a). String stability of interconnected systems. IEEE Trans. Aut. Contr., 41(3):349-357.
  16. Swaroop, D. and Hedrick, K. (1996a). String stability of interconnected systems. IEEE Trans. Aut. Contr., 41(3):349-357.
  17. Swaroop, D. and Hedrick, K. (1996b). String stability of interconnected systems. IEEE Trans. Aut. Contr., 41(3):349-357.
  18. Swaroop, D. and Hedrick, K. (1996b). String stability of interconnected systems. IEEE Trans. Aut. Contr., 41(3):349-357.
  19. Tangerman, F. M., Veerman, J. J. P., and Stosic, B. D. (2010). Asymmetric decentralized flocks. Submitted.
  20. Tangerman, F. M., Veerman, J. J. P., and Stosic, B. D. (2010). Asymmetric decentralized flocks. Submitted.
  21. Veerman, J. J. P. (2010). Stability of large flocks: an example. arXiv:1002.0768.
  22. Veerman, J. J. P. (2010). Stability of large flocks: an example. arXiv:1002.0768.
  23. Veerman, J. J. P., Caughman, J. S., Lafferriere, G., and Williams, A. (2005). Flocks and formations. J. Stat. Phys., 121(5-6):901-936.
  24. Veerman, J. J. P., Caughman, J. S., Lafferriere, G., and Williams, A. (2005). Flocks and formations. J. Stat. Phys., 121(5-6):901-936.
  25. Veerman, J. J. P., Stosic, B. D., and Tangerman, F. M. (2009). Automated traffic and the finite size resonance. J. Stat. Phys., 137(1):189-203.
  26. Veerman, J. J. P., Stosic, B. D., and Tangerman, F. M. (2009). Automated traffic and the finite size resonance. J. Stat. Phys., 137(1):189-203.
  27. Veerman, J. J. P. and Tangerman, F. M. (2010). Impulse stability of large flocks: an example. arXiv:1002.0782.
  28. Veerman, J. J. P. and Tangerman, F. M. (2010). Impulse stability of large flocks: an example. arXiv:1002.0782.
  29. Williams, A., Lafferriere, G., and Veerman, J. (2005). Stable motions of vehicle formations. In IEEE 44th Conf. on Decision and Contr., pages 72-77.
  30. Williams, A., Lafferriere, G., and Veerman, J. (2005). Stable motions of vehicle formations. In IEEE 44th Conf. on Decision and Contr., pages 72-77.
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Paper Citation


in Harvard Style

Veerman J. (2011). SYMMETRY AND STABILITY OF HOMOGENEOUS FLOCKS . In Proceedings of the 1st International Conference on Pervasive and Embedded Computing and Communication Systems - Volume 1: PECCS, ISBN 978-989-8425-48-5, pages 470-475. DOI: 10.5220/0003400204700475


in Harvard Style

Veerman J. (2011). SYMMETRY AND STABILITY OF HOMOGENEOUS FLOCKS . In Proceedings of the 1st International Conference on Pervasive and Embedded Computing and Communication Systems - Volume 1: PECCS, ISBN 978-989-8425-48-5, pages 470-475. DOI: 10.5220/0003400204700475


in Bibtex Style

@conference{peccs11,
author={J. J. P. Veerman},
title={SYMMETRY AND STABILITY OF HOMOGENEOUS FLOCKS},
booktitle={Proceedings of the 1st International Conference on Pervasive and Embedded Computing and Communication Systems - Volume 1: PECCS,},
year={2011},
pages={470-475},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003400204700475},
isbn={978-989-8425-48-5},
}


in Bibtex Style

@conference{peccs11,
author={J. J. P. Veerman},
title={SYMMETRY AND STABILITY OF HOMOGENEOUS FLOCKS},
booktitle={Proceedings of the 1st International Conference on Pervasive and Embedded Computing and Communication Systems - Volume 1: PECCS,},
year={2011},
pages={470-475},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003400204700475},
isbn={978-989-8425-48-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 1st International Conference on Pervasive and Embedded Computing and Communication Systems - Volume 1: PECCS,
TI - SYMMETRY AND STABILITY OF HOMOGENEOUS FLOCKS
SN - 978-989-8425-48-5
AU - Veerman J.
PY - 2011
SP - 470
EP - 475
DO - 10.5220/0003400204700475


in EndNote Style

TY - CONF
JO - Proceedings of the 1st International Conference on Pervasive and Embedded Computing and Communication Systems - Volume 1: PECCS,
TI - SYMMETRY AND STABILITY OF HOMOGENEOUS FLOCKS
SN - 978-989-8425-48-5
AU - Veerman J.
PY - 2011
SP - 470
EP - 475
DO - 10.5220/0003400204700475