zbMATH — the first resource for mathematics

On robust consensus of multi-agent systems with communication delays. (English) Zbl 1190.93003
Summary: Two robust consensus problems are considered for a multi-agent system with various disturbances. To achieve the robust consensus, two distributed control schemes for each agent, described by a second-order differential equation, are proposed. With the help of graph theory, the robust consensus stability of the multi-agent system with communication delays is obtained for both fixed and switching interconnection topologies. The results show the leaderless consensus can be achieved with some disturbances or time delays.

93A14 Decentralized systems
93C10 Nonlinear systems in control theory
94C15 Applications of graph theory to circuits and networks
PDF BibTeX Cite
Full Text: Link EuDML
[1] J. Bang-Jensen and G. Gutin: Digraphs Theory. Algorithms and Applications, Springer-Verlag, New York 2002. · Zbl 1001.05002
[2] M. G. Earl and S. H. Strogatz: Synchronization in oscillator networks with delayed coupling: A stability criterion. Phys. Rev. E 67 (2003), 036204.1-036204.4.
[3] C. Godsil and G. Royle: Algebraic Graph Theory. Springer-Verlag, New York 2001. · Zbl 0968.05002
[4] J. K. Hale and S. M. V. Lunel: Introduction to the Theory of Functional Differential Equations. Springer-Verlag, New York 1991.
[5] I. M. Havel: Sixty years of cybernetics: cybernetics still alive. Kybernetika 44 (2008), 314-327. · Zbl 1154.01305
[6] Y. Hong, G. Chen, and L. Bushnell: Distributed observers design for leader-following control of multi-agent networks. Automatica 44 (2008), 846-850. · Zbl 1283.93019
[7] R. Horn and C. Johnson: Matrix Analysis. Cambridge Univ. Press, New York 1985. · Zbl 0576.15001
[8] J. Hu and Y. Hong: Leader-following coordination of multi-agent systems with coupling time delays. Physica A 374 (2007), 853-863.
[9] J. Hu and X. Hu: Optimal target trajectory estimation and filtering using networked sensors. J. Systems Sci. Complexity 21 (2008), 325-336. · Zbl 1173.93377
[10] A. Jadbabaie, J. Lin, and A. S. Morse: Coordination of groups of mobile agents using nearest neighbor rules. IEEE Trans. Automat. Control 48 (2003), 988-1001. · Zbl 1364.93514
[11] S. Low, F. Paganini, and J. Doyle: Internet congestion control. IEEE Control Systems Magazine 32 (2002), 28-43. · Zbl 1061.93074
[12] Y. S. Moon, P. Park, W. H. Kwon, and Y. S. Lee: Delay-dependent robust stabilization of uncertain state-delayed systems. Internat. J. Control 74 (2001), 1447-1455. · Zbl 1023.93055
[13] L. Moreau: Stability of multiagent systems with time-dependent communication links. IEEE Trans. Automat. Control 50 (2005), 169-182. · Zbl 1365.93268
[14] R. Olfati-Saber, J. A. Fax, and R. M. Murray: Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95 (2007), 215-233. · Zbl 1376.68138
[15] R. Olfati-Saber and R. M. Murray: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Automat. Control 49 (2004), 1520-1533. · Zbl 1365.93301
[16] K. Peng and Y. Yang: Leader-following consensus problem with a varying-velocity leader and time-varying delays. Physica A 388 (2009), 193-208.
[17] W. Ren and R. W. Beard: Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans. Automat. Control 50 (2005), 655-661. · Zbl 1365.93302
[18] G. Shi and Y. Hong: Global target aggregation and state agreement of nonlinear multi-agent systems with switching topologies. Automatica 45 (2009), 1165-1175. · Zbl 1162.93308
[19] Y. Sun and J. Ruan: Consensus problems of multi-agent systems with noise perturbation. Chinese Phys. B 17 (2008), 4137-4141.
[20] T. Vicsek, A. Czirok, and E. B. Jacob, I. Cohen, and O. Schochet: Novel type of phase transitions in a system of self-driven particles. Phys. Rev. Lett. 75 (1995), 1226-1229.
[21] F. Xiao and L. Wang: Consensus protocols for discrete-time multi-agent systems with time-varying delays. Automatica 44 (2008), 2577-2582. · Zbl 1155.93312
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.