Advertisement

Soft Computing

, Volume 23, Issue 2, pp 707–714 | Cite as

Swarming movement of dynamical multi-agent systems with sampling control and time delays

  • Fusheng Wang
  • Hongyong YangEmail author
  • Yize Yang
Methodologies and Application
  • 71 Downloads

Abstract

In the complex environments, sampling control has been extensively applied in continue-time systems by means of digital sensors with high reliability and stability. In this paper, swarming movement (or containment consensus) of fractional-order multi-agent systems (FOMAS) with sampling control are studied. Firstly, the collaborative control of fractional-order multi-agent systems with multiple leaders and sapling data is analyzed in an undirected network without delays. A necessary and sufficient condition is presented for the bounded value of sampling period to ensure the containment consensus of FOMAS. Then, by applying Laplace transformation and stability theorem, containment consensus of distributed FOMAS with time delays is investigated in an undirected network. A necessary and sufficient condition is obtained for the bounded value of sampling period and a critical value of delays. Finally, numerical simulations are shown to verify the results.

Keywords

Swarming movement Containment control Multi-agent systems Fractional-order Sampling control Time delays 

Notes

Acknowledgements

Project supported by the National Natural Science Foundation of China (Grants Nos. 61673200, 61603172 and 61472172) and by the Natural Science Foundation of Shandong Province of China (Grant No. BS2014DX016).

Compliance with ethical standards

Conflict of interest

This paper has no conflicts of interest statements with other papers.

References

  1. Cao Y, Ren W (2010) Distributed coordination for fractional-order systems: dynamic interaction and absolute/relative damping. Syst Control Lett 43(3–4):233–240CrossRefzbMATHGoogle Scholar
  2. Cao Y, Li Y, Ren W, Chen YQ (2010) Distributed coordination of networked fractional-order systems. IEEE Trans Syst Man Cybern B Cybern 40(2):362–370CrossRefGoogle Scholar
  3. Cao Y, Stuart D, Ren W, Meng Z (2011) Distributed containment control for multiple autonomous vehicles with double-integrator dynamics: algorithms and experiments. IEEE Trans Control Syst Technol 19(4):929–938CrossRefGoogle Scholar
  4. Chen F, Chen ZQ, Xiang L, Liu Z, Yuan Z (2009) Reaching a consensus via pinning control. Automatica 45(5):1215–1220MathSciNetCrossRefzbMATHGoogle Scholar
  5. Chen YY, Wang ZZ, Zhang Y, Liu CL, Wei P (2016) Coordinated orbit-tracking control of second-order nonlinear agents with directed communication topologies. Int J Syst Sci 47(16):3929–3939CrossRefzbMATHGoogle Scholar
  6. Chen YY, Wang ZZ, Zhang Y, Liu CL, Wang Q (2017a) A geometric extension design for spherical formation tracking control of second-order agents in unknown spatiotemporal flowfields. Nonlinear Dyn 88(2):1173–1186Google Scholar
  7. Chen YY, Zhang Y, Wang ZZ (2017b) An adaptive backstepping design for formation tracking motion in an unknown Eulerian specification flowfield. J Frankl Inst 354:6217–6233Google Scholar
  8. Gu B, Sun X, Sheng Victor S (2016) Structural minimax probability machine. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2016.2544779
  9. Jadbabaie A, Lin J, Morse AS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control 48(6):988–1001MathSciNetCrossRefzbMATHGoogle Scholar
  10. Ji M, Ferrari-Trecate G, Egerstedt M, Buffa A (2008) Containment control in mobile networks. IEEE Trans Autom Control 53(8):1972–1975MathSciNetCrossRefzbMATHGoogle Scholar
  11. Li S, Du H, Lin X (2011) Finite-time consensus algorithm for multi-agent with double-integrator dynamics. Automatica 47(8):1706–1712MathSciNetCrossRefzbMATHGoogle Scholar
  12. Li J, Chen X, Li M et al (2014a) Secure deduplication with efficient and reliable convergent key management. IEEE Trans Parallel Distrib Syst 25(6):1615–1625Google Scholar
  13. Li J, Guan Z, Liao R et al (2014b) Impulsive containment control for second-order networked multi-agent systems with sampled information. Nonlinear Anal Hybrid Syst 12:93–103Google Scholar
  14. Li J, Yan H, Liu Z, Chen X, Huang X, Wong DS (2015) Location-sharing systems with enhanced privacy in mobile online social networks. IEEE Syst J. https://doi.org/10.1109/JSYST.2015.2415835
  15. Li P, Li J, Huang Z et al (2017) Multi-key privacy-preserving deep learning in cloud computing. Future Gener Comput Syst. https://doi.org/10.1016/j.future.2017.02.006
  16. Li J, Zhang Y, Chen X, Xiang Y (2018) Secure attribute-based data sharing for resource-limited users in cloud computing. Comput Secur 72:1–12.  https://doi.org/10.1016/j.cose.2017.08.007 CrossRefGoogle Scholar
  17. Lin P, Jia YM (2009) Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies. Automatica 45(9):2154–2158MathSciNetCrossRefzbMATHGoogle Scholar
  18. Liu J, Zhou J (2014) Distributed impulsive containment control for second-order multi-agent systems with multiple leaders. J Vib Control. https://doi.org/10.1177/1077546314547377
  19. Liu H, Xie G, Wang L (2012) Necessary and sufficient conditions for containment control of networked multi-agent systems. Automatica 48(7):1415–1422MathSciNetCrossRefzbMATHGoogle Scholar
  20. Meng Z, Ren W, You Z (2010) Distributed finite-time attitude containment control for multiple rigid bodies. Automatica 46(12):2092–2099MathSciNetCrossRefzbMATHGoogle Scholar
  21. Olfati-Saber R, Murray RM (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Control 49(9):1520–1533MathSciNetCrossRefzbMATHGoogle Scholar
  22. Podlubny I (1999) Fractional differential equations. Academic Press, San DiegozbMATHGoogle Scholar
  23. Ren W, Cao Y (2011) Distributed coordination of multi-agent networks. Springer, LondonCrossRefzbMATHGoogle Scholar
  24. Ren W, Beard RW, Atkins EM (2007) Information consensus in multivehicle cooperative control: collective group behavior through local interaction. IEEE Control Syst Mag 27(2):71–82CrossRefGoogle Scholar
  25. Tian YP, Liu C (2008) Consensus of multi-agent systems with diverse input and communication delays. IEEE Trans Autom Control 53(9):2122–2128MathSciNetCrossRefzbMATHGoogle Scholar
  26. Yang HY, Zhu X, Zhang S (2010) Consensus of second-order delayed multi-agent systems with leader-following. Eur J Control 16(2):188–199MathSciNetCrossRefzbMATHGoogle Scholar
  27. Yang HY, Zhang Z, Zhang S (2011) Consensus of second-order multi-agent systems with exogenous disturbances. Int J Robust Nonlinear Control 21(9):945–956MathSciNetCrossRefzbMATHGoogle Scholar
  28. Yang HY, Guo L, Zhang Y, Yao X (2014a) Movement consensus of complex fractional-order multi-agent systems. Acta Autom Sin 40(3):489–496Google Scholar
  29. Yang HY, Zhu X, Cao K (2014b) Distributed coordination of fractional order multi-agent systems with communication delays. Fract Calc Appl Anal 17(1):23–37. https://doi.org/10.2478/s13540-014-0153-9
  30. Yu J, Wang L (2010) Group consensus in multi-agent systems with switching topologies and communication delays. Syst Control Lett 59(6):340–348MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Information and Electrical EngineeringLudong UniversityYantaiChina

Personalised recommendations