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Consensus of Multi-agent System with Singular Dynamics and Time Delay

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Proceedings of the 2015 Chinese Intelligent Systems Conference

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE))

Abstract

In this paper, the consensus problem of high-order multi-agent systems with singular dynamics and time-varying time delay is investigated. By the restricted equivalent transformation, a differential-algebraic system is introduced which is equivalent to this singular system on consensus. Based on dynamic state information and time delay, a consensus protocol is proposed. A sufficient condition of consensus is given in terms of LMI. Furthermore, the consensus state is also obtained by calculating the solution of the subsystem. Finally, an example is presented to illustrate the theoretical results.

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References

  1. Olfati-Saber R (2006) Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans Autom Control 51(3):401–420

    Google Scholar 

  2. Xiao F, Wang L, Chen J (2009) Finite-time formation control for multi-agent systems. Automatica 45(11):2605–2611

    Article  MathSciNet  MATH  Google Scholar 

  3. Amarjeet S, Andreas K, Carlos G et al (2009) Efficient informative sensing using multiple robots. J Artif Intell Res 34:707–755

    MathSciNet  Google Scholar 

  4. Xiang H, Tian L (2011) Development of a low-cost agricultural remote sensing system based on an autonomous unmanned aerial vehicle. Biosyst Eng 108(2):174–190

    Article  MathSciNet  Google Scholar 

  5. Alex A, Albert D-G, Jurgen K et al (2008) Synchronization in complex networks. Phys Rep-Rev Sect Phys Lett 469(3):93–153

    MathSciNet  Google Scholar 

  6. Absessameud A, Tayebi A (2009) Attitude synchronization of a group of spacecraft without velocity measurement. IEEE Trans Autom Control 54(11):2642–2648

    Article  MathSciNet  MATH  Google Scholar 

  7. Olfati-Saber R, Fax JA et al (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95(1):215–233

    Google Scholar 

  8. Olfati-Saber R, Murray RM (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Control 49(9):1520–1533

    Google Scholar 

  9. Hong YG, JiangPing H, Gao LL (2006) Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42(7):1177–1182

    Article  MathSciNet  MATH  Google Scholar 

  10. Lin P, Jia YM (2008) Average consensus in networks of multi-agents with both switch topology and coupling time delay. Phys A-Stat Mech Appl 387(2):303–313

    Article  Google Scholar 

  11. Shang YL (2012) Finite-time consensus for multi-agent systems with fixed topologies. Int J Syst Sci 43(3):499–506

    Article  MathSciNet  MATH  Google Scholar 

  12. Li T, Zhang JF (2010) Consensus condition of multi-agent systems with time-varying topologies and stochastic communication noises. IEEE Trans Autom Control 55(9):2043–2057

    Article  MathSciNet  MATH  Google Scholar 

  13. Lin P, Jia YM (2010) Consensus of a class of second-order multi-agent systems with time-delay and jointly connected topologies. IEEE Trans Autom Control 53(3):778–784

    MathSciNet  MATH  Google Scholar 

  14. Zhu W, Cheng DZ (2010) Leader-following consensus of second-order agents with multiple time-varying delays. Automatica 46(12):1994–1999

    Article  MathSciNet  MATH  Google Scholar 

  15. He W, Cao J (2011) Consensus control for high-order multi-agent systems. IET Control Theory Appl 5(1):231–238

    Article  MathSciNet  Google Scholar 

  16. Jiang FC, Wang L (2010) Consensus seeking of high-order dynamic multi-agent systems with fixed and switching topologies. Int J Control 83(2):404–420

    Article  MathSciNet  MATH  Google Scholar 

  17. Tian YP, Zhang Y (2012) High-order consensus of heterogeneous multi-agent systems with unknown communication delays. Automatica 48(6):1205–1212

    Article  MathSciNet  MATH  Google Scholar 

  18. Li M, Li QQ (2014) Admissible consensus of multi-agent singular systems. Asian J Control 16(4):1169–1178

    Article  MathSciNet  MATH  Google Scholar 

  19. Xi JX, Shi ZY, Zhong YS (2012) Admissible consensus and consensualization of high-order linear time-invariant singular swarm systems. Phys A 391:5839–5849

    Article  Google Scholar 

  20. Xi JX, Yao Y, Liu GB et al (2014) Guaranteed-cost consensus for singular multi-agent systems with switching topologies. IEEE Trans Circuits Syst-I: Regul Pap 61(5):1531–1541

    Article  MathSciNet  Google Scholar 

  21. JianXiang X, FanLin M, ZongYing S et al (2014) Delay-dependent admissible consensualization for singular time-delayed swarm systems. Syst Control Lett 61(11):1089–1096

    MathSciNet  MATH  Google Scholar 

  22. Godsil C, Royle G (2001) Algebraic graph theory. Springer, NewYork

    Book  MATH  Google Scholar 

  23. Ren W, Beard RW (2005) Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Trans Autom Control 50(5):655–661

    Article  MATH  Google Scholar 

  24. Dai L (1989) Singular control systems. Springer, NewYork

    Book  MATH  Google Scholar 

  25. YuanGong S, Long W, GuangMing X (2008) Average consen-sus in networks of dynamic agents with switching topologies and multiple time-varying de-lays. Syst Control Lett 57(2):175–183

    Article  Google Scholar 

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (Grant No.61174094,61273138), and the Tianjin Natural Science Foundation of China (Grant No.14JCYBJC18700, 14JCZDJC39300).

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Authors and Affiliations

  1. College of Computer and Control Engineering, Nankai University, Tianjin, 300071, China

    Hua Geng, Zengqiang Chen & Zhongxin Liu

  2. Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin, 300071, China

    Hua Geng, Zengqiang Chen & Zhongxin Liu

  3. College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Zengqiang Chen & Qing Zhang

Authors
  1. Hua Geng
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  2. Zengqiang Chen
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  3. Zhongxin Liu
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  4. Qing Zhang
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Corresponding author

Correspondence to Hua Geng .

Editor information

Editors and Affiliations

  1. Beihang University, Beijing, China

    Yingmin Jia

  2. Beijing University of Posts and Telecommunications, Beijing, China

    Junping Du

  3. Tsinghua University, Beijing, China

    Hongbo Li

  4. University of Science & Technology Beijing, Beijing, China

    Weicun Zhang

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Geng, H., Chen, Z., Liu, Z., Zhang, Q. (2016). Consensus of Multi-agent System with Singular Dynamics and Time Delay. In: Jia, Y., Du, J., Li, H., Zhang, W. (eds) Proceedings of the 2015 Chinese Intelligent Systems Conference. Lecture Notes in Electrical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48386-2_19

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  • DOI: https://doi.org/10.1007/978-3-662-48386-2_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48384-8

  • Online ISBN: 978-3-662-48386-2

  • eBook Packages: EngineeringEngineering (R0)

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