Consensus of Multi-Agent Systems under the Special Consensus Protocols

Two consensus problems are considered in this
paper. One is the consensus of linear multi-agent systems with
weakly connected directed communication topology. The other
is the consensus of nonlinear multi-agent systems with strongly
connected directed communication topology. For the first problem,
a simplified consensus protocol is designed: Each child agent can
only communicate with one of its neighbors. That is, the real
communication topology is a directed spanning tree of the original
communication topology and without any cycles. Then, the necessary
and sufficient condition is put forward to the multi-agent systems can
be reached consensus. It is worth noting that the given conditions do
not need any eigenvalue of the corresponding Laplacian matrix of the
original directed communication network. For the second problem,
the feedback gain is designed in the nonlinear consensus protocol.
Then, the sufficient condition is proposed such that the systems can
be achieved consensus. Besides, the consensus interval is introduced
and analyzed to solve the consensus problem. Finally, two numerical
simulations are included to verify the theoretical analysis.

Authors:

• Konghe Xie

Keywords:

• Consensus
• multi-agent systems
• directed spanning tree
• the Laplacian matrix.

References:

[1] R. Olfati-Saber, J. A. Fax, and R. M. Murray, Consensus and cooperation
in networked multi-agent systems, Proc. IEEE, vol. 97, no. 1, pp. 215-233,
2007.
[2] Z. K. Li, Z. S. Duan, G. R. Chen, and Huang, L, Consensus of multiagent
systems and synchronization of complex networks: a unified viewpoint.
IEEE Transactions on Circuits and Systems. I. Regular Papers, vol. 57,
no. 1, pp. 213-224, 2010.
[3] Z. K. Li, X. D. Liu, P. Lin, and W, Ren, Consensus of linear multi-agent
systems with reduced-order observer-based protocols. Systems and
Control Letters, vol. 60, no. 7, pp. 510-516, 2011.
[4] Z. K. Li, W. Ren, X. D. Liu, and L. H. Xie, Distributed consensus of
linear multi-agent systems with adaptive dynamic protocols. Automatica,
vol. 49, no. 7, pp. 1986-1995, 2013.
[5] Y. M. Xin and Z. S. Cheng, r-consensus control for discrete-time
high-order multi-agent systems. IET Control Theory and Applications,
vol. 7, no. 17, pp. 2103-2109, 2013.
[6] Y. M. Xin and Z. S. Cheng, r-consensus control for higher-order
multi-agent systems with digraph. Asian Journal of Control, vol. 15, no.
5, pp. 1524-1530, 2013.
[7] Y. M. Xin and Z. S. Cheng, Consensus control in linear multiagent
systems with current and sampled partial relative states. Asian Journal
of Control, vol. 16, no. 4, pp. 1105-1111, 2014.
[8] W. W. Yu, G. R. Chen and M. Cao, Second-Order consensus for
multiagent systems with directed topologies and nonlinear dynamics.
IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 40, no. 3, pp. 881-891,
2010.
[9] Q. Song, F. Liu, J. D. Cao, and W. W. Yu, Pinning-controllability analysis
of complex networks: An M-matrix approach. IEEE Trans. Circuits Syst.
I, Reg. Papers, vol. 59, no. 11, pp. 2692-2701, 2012.
[10] Q. Song, F. Liu, J. D. Cao, and W. W. Yu, M-Matrix strategies for
pinning-controlled leader-following consensus in multiagent systems with
nonlinear dynamics. IEEE Transactions on Cybernetics, vol. 43, no. 6,
pp. 1688-1697, 2013.
[11] J. Cortes, Distributed algorithms for reaching consensus on general
functions. Automatica, vol. 44, no. 3, pp. 726-737, 2008.
[12] Y. Z. Chen, Y. R. Ge and Y. X. Zhang, Partial stability approach
to consensus problem of linear multi-agent Systems. Acta Automatica
Sinica, vol. 40, no. 11, pp. 2573-2584, 2014.
[13] H. K. Khalil, Nonlinear Systems, 3rd ed. Englewood Cliffs, NJ: Prentice
Hall, 2002.