Leader-following consensus of second-order nonlinear multi-agent systems with intermittent position measurements

Abstract

This work studies the leader-following consensus problem of second-order nonlinear multi-agent systems with aperiodically intermittent position measurements. Through the filter-based method, a novel intermittent consensus protocol without velocity measurements is designed for each follower exclusively based on the relative position measurements of neighboring agents. Under the common assumption that only relative position measurements between the neighboring agents are intermittently used, some consensus conditions are derived for second-order leader-following multi-agent systems with inherent delayed nonlinear dynamics. Moreover, for multi-agent systems without inherent delayed nonlinear dynamics, some simpler consensus conditions are presented. Finally, some simulation examples are presented to verify and illustrate the theoretical results.

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References

  1. 1

    Tanner H G, Jadbabaie A, Pappas G J. Flocking in fixed and switching networks. IEEE Trans Autom Control, 2007, 52: 863–868

    MathSciNet  Article  MATH  Google Scholar 

  2. 2

    Scardovi L, Sepulchre R. Synchronization in networks of identical linear systems. Automatica, 2009, 45: 2557–2562

    MathSciNet  Article  MATH  Google Scholar 

  3. 3

    Liu T F, Jiang Z P. Distributed formation control of nonholonomic mobile robots without global position measurements. Automatica, 2013, 49: 592–600

    MathSciNet  Article  MATH  Google Scholar 

  4. 4

    Ogren P, Fiorelli E, Leonard N E. Cooperative control of mobile sensor networks: adaptive gradient climbing in a distributed environment. IEEE Trans Autom Control, 2004, 49: 1292–1302

    MathSciNet  Article  MATH  Google Scholar 

  5. 5

    Ren W, Beard R W. Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Autom Control, 2005, 50: 655–661

    MathSciNet  Article  MATH  Google Scholar 

  6. 6

    Olfati-Saber R, Fax J A, Murray R M. Consensus and cooperation in networked multi-agent systems. Proc IEEE, 2007, 95: 215–233

    Article  MATH  Google Scholar 

  7. 7

    Yu W W, Chen G R, Cao M. Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. Automatica, 2010, 46: 1089–1095

    MathSciNet  Article  MATH  Google Scholar 

  8. 8

    Yu W W, Chen G R, Cao M, et al. Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics. IEEE Trans Syst Man Cybern B, 2010, 40: 881–891

    Article  Google Scholar 

  9. 9

    Liu Z X, Chen Z Q. Discarded consensus of network of agents with state constraint. IEEE Trans Autom Control, 2012, 57: 2869–2874

    MathSciNet  Article  MATH  Google Scholar 

  10. 10

    Ma L F, Wang Z D, Han Q L, et al. Consensus control of stochastic multi-agent systems: a survey. Sci China Inf Sci, 2017, 60: 120201

    MathSciNet  Article  Google Scholar 

  11. 11

    Hong Y G, Hu J P, Gao L. Tracking control for multi-agent consensus with an active leader and variable topology. Automatica, 2006, 42: 1177–1182

    MathSciNet  Article  MATH  Google Scholar 

  12. 12

    Zhu W, Cheng D Z. Leader-following consensus of second-order agents with multiple time-varying delays. Automatica, 2010, 46: 1994–1999

    MathSciNet  Article  MATH  Google Scholar 

  13. 13

    Wang F Y, Liu Z X, Chen Z Q. Leader-following consensus of switched multi-agent systems with general second-order dynamics. In: Proceedings of Chinese Automation Congress (CAC), Jinan, 2017. 743–747

    Google Scholar 

  14. 14

    Zhao B R, Peng Y J, Song Y N, et al. Sliding mode control for consensus tracking of second-order nonlinear multi-agent systems driven by Brownian motion. Sci China Inf Sci, 2018, 61: 070216

    MathSciNet  Article  Google Scholar 

  15. 15

    Wang F Y, Liu Z X, Chen Z Q. A novel leader-following consensus of multi-agent systems with smart leader. Int J Control Autom Syst, 2018, 16: 1483–1492

    Article  Google Scholar 

  16. 16

    Liu H Y, Xie G M, Wang L. Necessary and sufficient conditions for containment control of networked multi-agent systems. Automatica, 2012, 48: 1415–1422

    MathSciNet  Article  MATH  Google Scholar 

  17. 17

    Wang F Y, Yang H Y, Zhang S N, et al. Containment control for first-order multi-agent systems with time-varying delays and uncertain topologies. Commun Theory Phys, 2016, 66: 249–255

    MathSciNet  Article  MATH  Google Scholar 

  18. 18

    Wang F Y, Liu Z X, Chen Z Q. Mean square containment control of second-order multi-agent systems with jointly-connected topologies. In: Proceedings of the 36th Chinese Control Conference, Dalian, 2017. 8084–8089

    Google Scholar 

  19. 19

    Wang F Y, Yang H Y, Liu Z X, et al. Containment control of leader-following multi-agent systems with jointly-connected topologies and time-varying delays. Neurocomputing, 2017, 260: 341–348

    Article  Google Scholar 

  20. 20

    Wang F Y, Ni Y H, Liu Z X, et al. Containment control for general second-order multi-agent systems with switched dynamics. IEEE Trans Cybern, 2018. doi: 10.1109/TCYB.2018.2869706

    Google Scholar 

  21. 21

    Wen G H, Duan Z S, Yu W W, et al. Consensus in multi-agent systems with communication constraints. Int J Robust Nonlinear Control, 2012, 22: 170–182

    MathSciNet  Article  MATH  Google Scholar 

  22. 22

    Wen G H, Duan Z S, Ren W, et al. Distributed consensus of multi-agent systems with general linear node dynamics and intermittent communications. Int J Robust Nonlinear Control, 2014, 24: 2438–2457

    MathSciNet  Article  MATH  Google Scholar 

  23. 23

    Duan Z S, Huang N, Zhao Y. Leader-following consensus of second-order non-linear multi-agent systems with directed intermittent communication. IET Control Theory Appl, 2014, 8: 782–795

    MathSciNet  Article  Google Scholar 

  24. 24

    Li H J, Su H Y. Distributed consensus of multi-agent systems with nonlinear dynamics via adaptive intermittent control. J Franklin Inst, 2015, 352: 4546–4564

    MathSciNet  Article  MATH  Google Scholar 

  25. 25

    Huang N, Duan Z S, Zhao Y. Consensus of multi-agent systems via delayed and intermittent communications. IET Control Theory Appl, 2014, 9: 62–73

    MathSciNet  Article  Google Scholar 

  26. 26

    Wen G H, Duan Z S, Yu W W, et al. Consensus of second-order multi-agent systems with delayed nonlinear dynamics and intermittent communications. Int J Control, 2013, 86: 322–331

    MathSciNet  Article  MATH  Google Scholar 

  27. 27

    Qin W, Liu Z X, Chen ZQ. A novel observer-based formation for nonlinear multi-agent systems with time delay and intermittent communication. Nonlinear Dyn, 2015, 79: 1651–1664

    MathSciNet  Article  MATH  Google Scholar 

  28. 28

    Wang F Y, Liu Z X, Chen Z Q. Distributed containment control for second-order multiagent systems with time delay and intermittent communication. Int J Robust Nonlinear Control, 2018, 28: 5730–5746

    MathSciNet  Article  MATH  Google Scholar 

  29. 29

    Yu Z Y, Jiang H J, Hu C, et al. Consensus of second-order multi-agent systems with delayed nonlinear dynamics and aperiodically intermittent communications. Int J Control, 2017, 90: 909–922

    MathSciNet  Article  MATH  Google Scholar 

  30. 30

    Ren W. On consensus algorithms for double-integrator dynamics. IEEE Trans Autom Control, 2008, 53: 1503–1509

    MathSciNet  Article  MATH  Google Scholar 

  31. 31

    Abdessameud A, Tayebi A. On consensus algorithms for double-integrator dynamics without velocity measurements and with input constraints. Syst Control Lett, 2010, 59: 812–821

    MathSciNet  Article  MATH  Google Scholar 

  32. 32

    Hong Y G, Chen G R, Bushnell L. Distributed observers design for leader-following control of multi-agent networks. Automatica, 2008, 44: 846–850

    MathSciNet  Article  MATH  Google Scholar 

  33. 33

    Li J Z, Ren W, Xu S Y. Distributed containment control with multiple dynamic leaders for double-integrator dynamics using only position measurements. IEEE Trans Autom Control, 2012, 57: 1553–1559

    MathSciNet  Article  MATH  Google Scholar 

  34. 34

    Mei J, Ren W, Ma G. Distributed coordination for second-order multi-agent systems with nonlinear dynamics using only relative position measurements. Automatica, 2013, 49: 1419–1427

    MathSciNet  Article  MATH  Google Scholar 

  35. 35

    Kelly R. A simple set-point robot controller by using only position measurements. IFAC Proc Volumes, 1993, 26: 527–530

    Article  Google Scholar 

  36. 36

    Boyd S, Ghaoui L E, Feron E, et al. Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM, 1994

    Google Scholar 

  37. 37

    Wu M, He Y, She J. Stability Analysis and Robust Control of Time-Delay Systems. Berlin: Springer, 2010

    Google Scholar 

  38. 38

    Huang L. Linear Algebra in System and Control Theory. Beijing: Science Press, 1984

    Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61573200, 61573199).

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Correspondence to Zhongxin Liu.

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Wang, F., Liu, Z. & Chen, Z. Leader-following consensus of second-order nonlinear multi-agent systems with intermittent position measurements. Sci. China Inf. Sci. 62, 202204 (2019). https://doi.org/10.1007/s11432-018-9732-7

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Keywords

  • leader-following consensus
  • second-order multi-agent system
  • delayed nonlinear dynamics
  • distributed filter
  • intermittent measurements