Abstract
In this paper, the consensus problem of fractional-order multi-agent systems (FOMAS) with perturbation is considered. Both undirected and directed communication topologies are considered for FOMAS, where the fractional order \(0<\alpha <2\). By using the fractional-order stability theory and the inequality techniques, some consensus criteria are obtained. Besides, an example is given for illustration.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
DeGroot M (1974) Reaching a consensus. J Am Stat Assoc 69(345):118–121
Winkler R (1968) The consensus of subjective probability distributions. Manag Sci 15(2):61–75
Chen F, Chen Z, Xiang L, Liu Z, Yuan Z (2009) Reaching a consensus via pinning control. Automatica 45(5):1215–1220
Olfati-Saber R (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95(1):215–233
Sun Y, Wang L (2009) Consensus problems in networks of agents with dobble-integrator dynamics and time-varying delays. Int J Control 82(10):1937–1945
Liu Y, Jia Y (2010) Consensus problem of high-order multi-agent systems with external disturbances: an \(H_{\infty }\) analysis approach. Int J Robust Nonlinear Control 20(14):1579–1593
Cao Y, Li Y, Chen Y (2008) Distributed coordination algorithems for multiple fractional-order systems. In: IEEE conference on decision and control, pp 9–11
Cao Y, Li Y, Ren W, Chen Y (2010) Distributed coordination of networked fractional-order systems. IEEE Trans Syst Man Cybern 40(2):362–370
Song C, Cao J (2013) Consensus of fractional-order linear systems. In: 9th Asian control conference (ASCC), pp 1–4
Yin X, Yue D, Hu S (2013) Consensus of fractional-order heterogeneous multi-agent systems. IET Control Theory Appl 7(2):314–322
Shen J, Cao J (2012) Necessary and sufficient conditions for consensus of delayed fractional-order systems. Asian J Control 14(6):1690–1697
Li H (2012) Observer-type consensus protocol for a class of fractional-order uncertain multiagent systems. Abstr Appl Anal. doi:10.1155/2012/672346
Bai J, Wen G, Rahmani A, Yu Y (2015) Distributed formation control of fractional-order multi-agent systems with absolute damping and communication delay. Int J SystSci 46(13):2380–2392
Hammel D (1995) Formation flight as an energy saving mechanism. Israel J Zool 41(3):261–278
Yu Z, Jiang H, Hu C (2015) Leader-following consensus of fractional-order multi-agent systems under fixed topology. Neurocomputing 149:613–620
Yu Z, Jiang H, Hu C, Yu J (2015) Leader-following consensus of fractional-order multi-agent systems via adaptive pinning control. Int J Control 88(9):1746–1756
Wang J, Ma Q, Zeng L (2013) Observer-based synchronization in fractional-order leader-follower complex networks. Nonlinear Dyn 73(1):921–929
Sabatier J, Moze M, Farges C (2010) LMI stability conditions for fractional order systems. Comput Math Appl 59(5):1594–1609
Kilbas A, Srivastava H, Trujillo J (2006) Theory and appliciations of fractional differential equations. Elsevier, The Netherlands
Boyd S, Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadelphia
Acknowledgments
This work was supported by National Natural Science Foundation of Peoples Republic of China (Grants No. 61164004, No. 61473244, No. 11402223).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media Singapore
About this paper
Cite this paper
Yu, Z., Jiang, H., Hu, C. (2016). Leader-Following Consensus Problem of Fractional-Order Multi-agent Systems with Perturbation. In: Jia, Y., Du, J., Zhang, W., Li, H. (eds) Proceedings of 2016 Chinese Intelligent Systems Conference. CISC 2016. Lecture Notes in Electrical Engineering, vol 404. Springer, Singapore. https://doi.org/10.1007/978-981-10-2338-5_24
Download citation
DOI: https://doi.org/10.1007/978-981-10-2338-5_24
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-2337-8
Online ISBN: 978-981-10-2338-5
eBook Packages: Computer ScienceComputer Science (R0)