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

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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Graph Connectivity-free Consensus Algorithm for State-coupled Linear Multi-agent Systems: Adaptive Approach

적응 제어를 이용하여 그래프 연결성을 배제시킨 선형 다개체 시스템의 상태변수 일치 알고리듬

  • 김지수 (ASRI, 서울대학교 전기컴퓨터공학부) ;
  • 김홍근 (ASRI, 서울대학교 전기컴퓨터공학부) ;
  • 심형보 (ASRI, 서울대학교 전기컴퓨터공학부) ;
  • 백주훈 (광운대학교 로봇학부)
  • Received : 2012.04.30
  • Accepted : 2012.06.20
  • Published : 2012.07.01
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Abstract

This paper studies asymptotic consensus problem for linear multi-agent systems. We propose a distributed state feedback control algorithm for solving the problem under fixed and undirected network communication. In contrast with the conventional algorithms that use global information (e.g., graph connectivity), the proposed algorithm only uses local information from neighbors. The principle for achieving asymptotic consensus is that, for each agent, a distributed update law gradually increases the coupling gain of LQR-type feedback and thus, the overall stability of the multi-agent system is recovered by the gain margin of LQR.

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References

  1. 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, 2005. https://doi.org/10.1016/j.sysconle.2005.02.004
  2. C. T. Chen, Linear System Theory and Design, 3rd edition, Oxford University Press, 1999.
  3. F. Cucker and S. Smale, "Emergent behavior in flocks," IEEE Transactions on Automatic Control, vol. 52, no. 5, pp. 852-862, 2007. https://doi.org/10.1109/TAC.2007.895842
  4. 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, 2004. https://doi.org/10.1109/TAC.2004.834433
  5. C. D. Godsil and G. Royle, Algebraic Graph Theory, Springer, Graduate Texts in Mathematics, vol. 207, 2001.
  6. H. K. Khalil, Nonlinear Systems, 3rd Ed., Prentice Hall, New Jersey, 2002.
  7. J. Kim, H. Kim, H. Shim, and J. Back, "Distributed adaptive control algorithm for state consensus of linear multi-agent systems," Proc. of the 27th ICROS Annual Conference, pp. 309-310, April 2012.
  8. J. Kim, H. Kim, H. Shim, and J. Back, "Output consensus of non-identical and stabilizable linear systems having the same transfer matrix," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 17, no. 9, pp. 857-862, 2011. https://doi.org/10.5302/J.ICROS.2011.17.9.857
  9. H. Kim, "Consensus and synchronization among output- coupled identical and non-identical linear systems through fast switching network," Ph.D. thesis, Seoul National University, Department of Electrical Engineering and Computer Science, South Korea, 2012.
  10. H. 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. 222-426, 2010. https://doi.org/10.5302/J.ICROS.2010.16.3.222
  11. 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, 2011. https://doi.org/10.1109/TAC.2010.2088710
  12. Z. Li, X. Liu, W. Ren, and M. Fu, "Consensus of multi- agent systems with general linear and lipschitz nonlinear dynamics using distributed adaptive protocols," arXiv:1109.3799v1[cs.SY] http://arxiv.org/abs/1109.3799
  13. Z. Li, X. Liu, W. Ren, and L. Xie, "Decentralized consensus of linear multi-agent systems with adaptive dynamic protocols," arXiv:1109.3838v2[cs.SY] http://arxiv.org/abs/1109.3838.
  14. W. Ren, R. W. Beard, and E. M. Atkins, "Information consensus in multi-vehicle cooperative control: collective group behavior through local interaction," IEEE Control Systems Magazine, vol. 27, no. 2, pp. 71-82, 2007. https://doi.org/10.1109/MCS.2007.338264
  15. C. W. Reynolds, "Flocks, Herds, and schools: a distributed behavioral model," Computer Graphics, vol. 21, no. 4, pp. 25-34, 1987. https://doi.org/10.1145/37402.37406
  16. L. Scardovi and R. Sepulchre, "Synchronization in networks of identical linear systems," Automatica, vol. 45, no. 11, pp. 2557-2562, 2009. https://doi.org/10.1016/j.automatica.2009.07.006
  17. 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, 2009. https://doi.org/10.1016/j.automatica.2009.07.022
  18. 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, 2010. https://doi.org/10.1007/s12555-010-0623-8
  19. S. E. Tuna, "LQR-based coupling gain for synchronization of linear systems," arXiv:0801. 3390v1[math.OC] http://arxiv.org/abs/0801.3390, 2008.
  20. P. Wieland, "From static to dynamic couplings in consensus and synchronization among identical and non-identical systems," Ph.D. thesis, University of Stuttgart, Institute for Systems Theory and Automatic Control, Germany, 2011.
  21. P. Yang, R. A. Freeman, G. J. Gordon, K. M. Lynch, S. S. Srinivasa, and R. Sukthankar, "Decentralized estimation and control of graph connectivity for mobile sensor networks," Automatica, vol. 46, no. 2, pp. 390-396, 2010. https://doi.org/10.1016/j.automatica.2009.11.012