Robust Stabilization against Unknown Consensus Network
This paper studies a robust stabilization problem of a
single agent in a multi-agent consensus system composed of identical
agents, when the network topology of the system is completely
unknown. It is shown that the transfer function of an agent in a
consensus system can be described as a multiplicative perturbation
of the isolated agent transfer function in frequency domain. From an
existing robust stabilization result, we present sufficient conditions for
a robust stabilization of an agent against unknown network topology.
[1] H. G. Tanner, "On the controllability of nearest neighbor
interconnections,” in Proceeding of the 43rd Conf. Decision Control,
Atlantis, Bahamas, December, 2004, pp. 2467–2472.
[2] A. Rahmani, M. Ji, M. Mesbahi, and M. Egerstedt, "Controllability
of multi-agent systems from a graph-theoretic perspective,” SIAM J.
Control Optim., vol. 48, no. 1, pp. 162–186, 2009.
[3] S. Martini, M. Egerstedt, and A. Bicchi, "Controllability analysis of
multi-agent systems using relaxed equitable partitions,” Int. J. Systems,
Control and Communications, vol. 2, pp. 100–121, 2010.
[4] M. Ji, A. Muhammad, and M. Egerstedt, "Leader-based multi-agent
coordination: Controllability and optimal control,” in American Control
Conference, Minneapolis, June 14-16, 2006.
[5] X. Li, X. Wang, and G. Chen, "Pinning a complex dynamical network
to its equilibrium,” IEEE Transaction on Circuits and Systems I, vol. 51,
no. 10, pp. 2074–2087, 2004.
[6] F. Chen, Z. Cen, L. Xiang, Z. Liu, and Z. Yuan, "Reaching a consensus
via pinning control,” Automatica, vol. 45, pp. 1215–1220, 2009.
[7] T. Chen, X. Liu, and W. Lu, "Pinning complex networks by a single
controller,” IEEE Transaction on Circuits and Systems I, vol. 54, pp.
1317–1326, 2007.
[8] W. Yua, G. Chena, and J. L¨u, "On pinning synchronization of complex
dynamical networks,” Automatica, vol. 45, pp. 429–435, 2009.
[9] J. Zhou, Q. Wu, and L. Xiang, "Pinning complex delayed dynamical
networks by a single impulsive controller,” IEEE Transaction on Circuits
and Systems I, vol. 58, no. 12, 2011.
[10] M.-G. Yoon, "Single agent control for multi-agent dynamical consensus
systems,” IET Control Theory & Applications, vol. 6, no. 10, p.
14781485, 2012.
[11] ——, "Single agent control for cyclic consensus systems,” International
Journal of Control, Automation, and Systems, vol. 11, no. 2, pp.
243–249, 2013.
[12] K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. New
Jersey: Prentice Hall, 1996.
[13] R. Merris, "Laplacian matrices of graphs: A survey,” Linear Algebra
and Its Applications, vol. 197-198, pp. 143–176, 1994.
[1] H. G. Tanner, "On the controllability of nearest neighbor
interconnections,” in Proceeding of the 43rd Conf. Decision Control,
Atlantis, Bahamas, December, 2004, pp. 2467–2472.
[2] A. Rahmani, M. Ji, M. Mesbahi, and M. Egerstedt, "Controllability
of multi-agent systems from a graph-theoretic perspective,” SIAM J.
Control Optim., vol. 48, no. 1, pp. 162–186, 2009.
[3] S. Martini, M. Egerstedt, and A. Bicchi, "Controllability analysis of
multi-agent systems using relaxed equitable partitions,” Int. J. Systems,
Control and Communications, vol. 2, pp. 100–121, 2010.
[4] M. Ji, A. Muhammad, and M. Egerstedt, "Leader-based multi-agent
coordination: Controllability and optimal control,” in American Control
Conference, Minneapolis, June 14-16, 2006.
[5] X. Li, X. Wang, and G. Chen, "Pinning a complex dynamical network
to its equilibrium,” IEEE Transaction on Circuits and Systems I, vol. 51,
no. 10, pp. 2074–2087, 2004.
[6] F. Chen, Z. Cen, L. Xiang, Z. Liu, and Z. Yuan, "Reaching a consensus
via pinning control,” Automatica, vol. 45, pp. 1215–1220, 2009.
[7] T. Chen, X. Liu, and W. Lu, "Pinning complex networks by a single
controller,” IEEE Transaction on Circuits and Systems I, vol. 54, pp.
1317–1326, 2007.
[8] W. Yua, G. Chena, and J. L¨u, "On pinning synchronization of complex
dynamical networks,” Automatica, vol. 45, pp. 429–435, 2009.
[9] J. Zhou, Q. Wu, and L. Xiang, "Pinning complex delayed dynamical
networks by a single impulsive controller,” IEEE Transaction on Circuits
and Systems I, vol. 58, no. 12, 2011.
[10] M.-G. Yoon, "Single agent control for multi-agent dynamical consensus
systems,” IET Control Theory & Applications, vol. 6, no. 10, p.
14781485, 2012.
[11] ——, "Single agent control for cyclic consensus systems,” International
Journal of Control, Automation, and Systems, vol. 11, no. 2, pp.
243–249, 2013.
[12] K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. New
Jersey: Prentice Hall, 1996.
[13] R. Merris, "Laplacian matrices of graphs: A survey,” Linear Algebra
and Its Applications, vol. 197-198, pp. 143–176, 1994.
@article{"International Journal of Electrical, Electronic and Communication Sciences:67457", author = "Myung-Gon Yoon and Jung-Ho Moon and Tae Kwon Ha", title = "Robust Stabilization against Unknown Consensus Network", abstract = "This paper studies a robust stabilization problem of a
single agent in a multi-agent consensus system composed of identical
agents, when the network topology of the system is completely
unknown. It is shown that the transfer function of an agent in a
consensus system can be described as a multiplicative perturbation
of the isolated agent transfer function in frequency domain. From an
existing robust stabilization result, we present sufficient conditions for
a robust stabilization of an agent against unknown network topology.
", keywords = "Multi-agent System, Robust Stabilization, Transfer Function.", volume = "8", number = "6", pages = "895-4", }
