Skip to main content

Leader-Following Consensus of Discrete-Time Multi-agent Systems with a Smart Leader

  • Conference paper
  • First Online:
Proceedings of 2019 Chinese Intelligent Systems Conference (CISC 2019)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 592))

Included in the following conference series:

  • 1008 Accesses

Abstract

In this paper, the consensus problem of discrete-time general linear multi-agent systems with a smart leader is studied. Unlike the previous works, an objective function is designed to decide whether the leader can receive information from the followers, with the purpose of effectively reducing the controller’s energy consumption. In order to track the desired target state, a new distributed control protocol is proposed for the multi-agent systems. By utilizing the Lyapunov function technology, some new sufficient conditions are established, which can ensure the leader-following consensus for discrete-time multi-agent systems with fixed topology and switching topology. In addition, the corresponding gain matrices are also obtained. Finally, simulation results are provided to demonstrate the theoretical results.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 299.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Huang JS, Wen CY, Wang W, Jiang ZP (2014) Adaptive output feedback tracking control of a nonholonomic mobile robot. Automatica 50(3):821–831. https://doi.org/10.1016/j.automatica.2013.12.036

    Article  MathSciNet  MATH  Google Scholar 

  2. Lin F, Fardad M, Jovanovic MR (2012) Optimal control of vehicular formations with nearest neighbor interactions. IEEE Trans Autom Control 57(9):2203–2218. https://doi.org/10.1109/TAC.2011.2181790

    Article  MathSciNet  MATH  Google Scholar 

  3. 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. https://doi.org/10.1109/tac.2004.834113

    Article  MathSciNet  MATH  Google Scholar 

  4. Yu WW, Chen GR, Cao M, Kurths J (2009) Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics. IEEE Trans Syst Man Cybern-Part B: Cybern 40(3):881–891. https://doi.org/10.1109/TSMCB.2009.2031624

    Article  Google Scholar 

  5. Wang FY, Liu ZX, Chen ZQ (2018) A novel leader-following consensus of multi-agent systems with smart leader. Int J Control Autom Syst 16(4):1483–1492. https://doi.org/10.1007/s12555-017-0266-0

    Article  Google Scholar 

  6. Song Q, Cao JD, Yu WW (2010) Second-order leader-following consensus of nonlinear multi-agent systems via pinning control. Syst Control Lett 59(9):553–562. https://doi.org/10.1016/j.sysconle.2010.06.016

    Article  MathSciNet  MATH  Google Scholar 

  7. Cao YC, Ren W (2012) Distributed coordinated tracking with reduced interaction via a variable structure approach. IEEE Trans Autom Control 57(1):33–48. https://doi.org/10.1109/tac.2011.2146830

    Article  MathSciNet  MATH  Google Scholar 

  8. Wu J, Li HQ, Chen X (2017) Leader-following consensus of nonlinear discrete-time multi-agent systems with limited communication channel capacity. J Franklin Inst 354(10):4179–4195. https://doi.org/10.1016/j.jfranklin.2017.03.005

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhou JP, Sang CY, Li X, Fang MY, Wang Z (2018) \(H_{\infty }\) consensus for nonlinear stochastic multi-agent systems with time delay. Appl Math Comput 325:41–58. https://doi.org/10.1016/j.amc.2017.12.020

    Article  MathSciNet  Google Scholar 

  10. Quan Y, Chen W, Wu ZH, Peng L (2018) Distributed fault detection and isolation for leader-follower multi-agent systems with disturbances using observer techniques. Nonlinear Dyn 93(2):863–871. https://doi.org/10.1007/s11071-018-4232-z

    Article  MATH  Google Scholar 

  11. Huang N, Duan ZS, Chen GR (2016) Some necessary and sufficient conditions for consensus of second-order multi-agent systems with sampled position data. Automatica 63:148–155. https://doi.org/10.1016/j.automatica.2015.10.020

    Article  MathSciNet  MATH  Google Scholar 

  12. Li ZK, Liu XD, Lin P, Ren W (2011) Consensus of linear multi-agent systems with reduced-order observer-based protocols. Syst Control Lett 60(7):510–516. https://doi.org/10.1016/j.sysconle.2011.04.008

    Article  MathSciNet  MATH  Google Scholar 

  13. Gao LX, Xu BB, Li JW, Zhang H (2015) Distributed reduced-order observer-based approach to consensus problems for linear multi-agent systems. IET Control Theory Appl 9(5):784–792. https://doi.org/10.1049/iet-cta.2013.1104

    Article  MathSciNet  Google Scholar 

  14. Liu HG, Liu ZX, Chen ZQ (2017) Leader-following consensus of second-order multi-agent systems with a smart leader. In: 36th Chinese control conference, Nanchang, pp 8090–8095. https://doi.org/10.23919/ChiCC.2017.8028637

  15. Wonham WM (1985) Linear multivariable control. Springer, Heidelberg. https://doi.org/10.1007/978-1-4612-1082-5_4

    Book  MATH  Google Scholar 

  16. Semsar-Kazerooni E, Khorasani K (2011) Switching control of a modified leader-follower team of agents under the leader and network topological changes. IET Control Theory Appl 5(12):1369–1377. https://doi.org/10.3182/20080706-5-kr-1001.00262

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 61573200, 61573199).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhongxin Liu .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Liang, S., Wang, F., Liu, Z., Chen, Z. (2020). Leader-Following Consensus of Discrete-Time Multi-agent Systems with a Smart Leader. In: Jia, Y., Du, J., Zhang, W. (eds) Proceedings of 2019 Chinese Intelligent Systems Conference. CISC 2019. Lecture Notes in Electrical Engineering, vol 592. Springer, Singapore. https://doi.org/10.1007/978-981-32-9682-4_27

Download citation

Publish with us

Policies and ethics