Robust Stabilization against Unknown Consensus Network

Authors: Myung-Gon Yoon, Jung-Ho Moon, Tae Kwon Ha

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1337249

References:

[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.