Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지
DOI QR코드

DOI QR Code

Output Consensus of Non-identical and Stabilizable Linear Systems Having the Same Transfer Matrix

동일한 전달 행렬을 가지는 안정화 가능한 이종 시스템들의 출력 일치

  • 김지수 (ASRI, 서울대학교 전기공학부) ;
  • 김홍근 (ASRI, 서울대학교 전기공학부) ;
  • 심형보 (ASRI, 서울대학교 전기공학부) ;
  • 백주훈 (광운대학교 로봇학부)
  • Received : 2011.07.08
  • Accepted : 2011.08.09
  • Published : 2011.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper studies the output consensus problem for a class of heterogeneous linear multi-agent systems under a fixed directed communication network. The dynamics, as well as its dimension, of each agent can widely differ from the others, but all the agents are assumed to have the same transfer matrix. In addition, only the system outputs are constrained to be delivered through the network. Under these conditions, we show that the output consensus is reached by a group of identical controllers, which is designed to achieve the state consensus for the homogeneous multi-agent system obtained from the minimal realization of the transfer matrix. Finally, an example is given to demonstrate the proposed result.

Keywords

References

  1. C. I. Byrnes, F. D. Priscoli, and A. Isidori, Output Regulation of Uncertain Nonlinear Systems, Birkhauser, 1997.
  2. J. S. Caughman, G. Lafferriere, J. J. P. Veerman, and A. Williams, "Decentralized control of vehicle formations," Systems and Control Letters, vol. 54, no. 9, pp. 899-910, Sep. 2005. https://doi.org/10.1016/j.sysconle.2005.02.004
  3. C.-T. Chen, Linear System Theory and Design, 3rd Ed., Oxford University Press, 1999.
  4. F. Cucker and S. Smale, "Emergent behavior in flocks," IEEE Transactions on Automatic Control, vol. 52, no. 5, pp. 852-862, May 2007. https://doi.org/10.1109/TAC.2007.895842
  5. J. A. Fax and R. M. Murray, "Information flow and cooperative control of vehicle formations," IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1465-1476, Sep. 2004. https://doi.org/10.1109/TAC.2004.834433
  6. B. A. Francis and W. M. Wonham, "The internal model principle of control theory," Automatica, vol. 12, no. 5, pp. 457-465, Sep. 1976. https://doi.org/10.1016/0005-1098(76)90006-6
  7. H. Kim, S. Kim, H. Shim, and J. Back, "Order reduction paradigm for consensus of neutrally stable multi-agent systems," Journal of Institute of Control, Robotics, and Systems (in Korean), vol. 16, no. 3, pp. 222-226, Mar. 2010. https://doi.org/10.5302/J.ICROS.2010.16.3.222
  8. H. Kim, H. Shim, J. Back, and J. H. Seo, "Consensus of multi-agent systems under periodic time-varying network," Proc. of the 8th IFAC Symposium on Nonlinear Control Systems, pp. 155-160, Sep. 2010.
  9. H. Kim, H. Shim, and J. H. Seo, "Output consensus of heterogeneous uncertain linear multi-agent systems," IEEE Transactions on Automatic Control, vol. 56, no. 1, pp. 200-206, Jan. 2011. https://doi.org/10.1109/TAC.2010.2088710
  10. J. Kim, H. Kim, H. Shim, and J. Back, "Output consensus of heterogeneous linear multi-agent systems having the same transfer matrix," Proc. of the 26th ICROS Annual Conference, pp. 575-576, May 2011.
  11. R. Olfati-Saber and J. S. Shamma, "Consensus filters for sensor networks and distributed sensor fusion," Proc. of the 44th IEEE Conference on Decision Control and European Control Conference, pp. 6698-6703, Dec. 2005. https://doi.org/10.1109/CDC.2005.1583238
  12. B. S. Park and J. B. Park, "Leader-following based adaptive formation control for multiple mobile robots," Journal of Institute of Control, Robotics, and Systems (in Korean), vol. 16, no. 5, pp. 428-432, May 2010. https://doi.org/10.5302/J.ICROS.2010.16.5.428
  13. W. Ren, R. W. Beard, and E. M. Atkins, "Information consensus in multivehicle cooperative control: collective group behavior through local interaction," IEEE Control Systems Magazine, vol. 27, no. 2, pp. 71-82, Apr. 2007. https://doi.org/10.1109/MCS.2007.338264
  14. C. W. Reynolds, "Flocks, herds, and schools: a distributed behavioral model," Computer Graphics, vol. 21, no. 4, pp. 25-34, Jul. 1987. https://doi.org/10.1145/37402.37406
  15. L. Scardovi and R. Sepulchre, "Synchronization in networks of identical linear systems," Automatica, vol. 45, no. 11, pp. 2557-2562, Nov. 2009. https://doi.org/10.1016/j.automatica.2009.07.006
  16. J. H. Seo, H. Shim, and J. Back, "Consensus of high-order linear systems using dynamic output feedback compensator: low gain approach," Automatica, vol. 45, no. 11, pp. 2659-2664, Nov. 2009. https://doi.org/10.1016/j.automatica.2009.07.022
  17. J. H. Seo, H. Shim, and J. Back, "Reduced-order consensus controllers for output-coupled SISO linear systems," International Journal of Control, Automation, and Systems, vol. 8, no. 6, pp. 1356-1363, Dec. 2010. https://doi.org/10.1007/s12555-010-0623-8
  18. S. E. Tuna, "LQR-based coupling gain for synchronization of linear systems," arXiv:0801. 3390v1[math.OC] http://arxiv.org/abs/0801.3390, Feb. 2008.
  19. D. Vengertsev, H. Kim, H. Shim, and J. H. Seo, "Consensus of output-coupled linear multi-agent systems under frequently connected network," Proc. of the 49th IEEE Confernece on Decision and Control, pp. 4559-4564, Dec. 2010. https://doi.org/10.1109/CDC.2010.5717998
  20. P. Wieland, "From Static to Dynamic Couplings in Consensus and Synchronization Among Identical and Non-Identical Systems," Ph.D. Dissertation, Institute for Systems Theory and Automatic Control, University of Stuttgart, Germany, 2011.
  21. P. Wieland and F. Allgöwer, "An internal model principle for consensus in heterogeneous linear multi-agent systems," Proc. of the 1st IFAC Workshop on Estimation and Control of Networked Systems, pp. 7-12, Sep. 2009.
  22. P. Wieland, R. Sepulchre, and F. Allgower, "An internal model is necessary and sufficient for linear output synchronization," Automatica, vol. 47, no. 5, pp. 1068-1074, May 2011. https://doi.org/10.1016/j.automatica.2011.01.081

Cited by

  1. Formation Control Algorithm for Coupled Unicycle-Type Mobile Robots Through Switching Interconnection Topology vol.18, pp.5, 2012, https://doi.org/10.5302/J.ICROS.2012.18.5.439