Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Finite-time and fixed-time consensus problems for second-order multi-agent systems with reduced state information

Abstract

This paper studies the fixed-time consensus (FixTC) and connectivity-preserving finite-time consensus (FinTC) protocol designs for second-order multi-agent systems using output information only. Herein, a distributed FixTC protocol based on the Lyapunov stability and bi-limit homogeneity approaches is proposed with the aid of an auxiliary system. Then, when the graph is state-dependent, i.e., the agents have limited sensing and communication ranges, a connectivity-preserving FinTC is proposed by designing a mechanism suitable for this purpose. Theoretical analysis and several simulations are presented to verify the effectiveness of the proposed protocols.

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

References

  1. 1

    Gazi V, Passino K M. Stability analysis of social foraging swarms. IEEE Trans Syst Man Cybern B, 2004, 34: 539–557

  2. 2

    Olfati-Saber R. Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans Automat Contr, 2006, 51: 401–420

  3. 3

    Dimarogonas D V, Kyriakopoulos K J. On the rendezvous problem for multiple nonholonomic agents. IEEE Trans Automat Contr, 2007, 52: 916–922

  4. 4

    Fax J A, Murray R M. Information flow and cooperative control of vehicle formations. IEEE Trans Automat Contr, 2004, 49: 1453–1464

  5. 5

    Lin Z L. Control design in the presence of actuator saturation: from individual systems to multi-agent systems. Sci China Inf Sci, 2019, 62: 026201

  6. 6

    Yu Y G, Zeng Z W, Li Z K, et al. Event-triggered encirclement control of multi-agent systems with bearing rigidity. Sci China Inf Sci, 2017, 60: 110203

  7. 7

    Yu W W, Wang H, Hong H F, et al. Distributed cooperative anti-disturbance control of multi-agent systems: an overview. Sci China Inf Sci, 2017, 60: 110202

  8. 8

    Yu W W, Wen G H, Chen G R, et al. Distributed Cooperative Control of Multi-agent Systems. Singapore: Wiley/Higher Education Press, 2016

  9. 9

    Cortés J. Finite-time convergent gradient flows with applications to network consensus. Automatica, 2006, 42: 1993–2000

  10. 10

    Liu X Y, Lam J, Yu W W, et al. Finite-time consensus of multiagent systems with a switching protocol. IEEE Trans Neural Netw Learn Syst, 2016, 27: 853–862

  11. 11

    Wang X L, Hong Y G. Finite-time consensus for multi-agent networks with second-order agent dynamics. IFAC Proc Vol, 2008, 41: 15185–15190

  12. 12

    Khoo S Y, Xie L H, Man Z H. Robust finite-time consensus tracking algorithm for multirobot systems. IEEE/ASME Trans Mechatron, 2009, 14: 219–228

  13. 13

    Li S H, Du H B, Lin X Z. Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics. Automatica, 2011, 47: 1706–1712

  14. 14

    Du H B, He Y G, Cheng Y Y. Finite-time synchronization of a class of second-order nonlinear multi-agent systems using output feedback control. IEEE Trans Circ Syst I, 2014, 61: 1778–1788

  15. 15

    Yu W W, Wang H, Cheng F, et al. Second-order consensus in multiagent systems via distributed sliding mode control. IEEE Trans Cybern, 2017, 47: 1872–1881

  16. 16

    Wang H, Yu W W, Wen G H, et al. Finite-time bipartite consensus for multi-agent systems on directed signed networks. IEEE Trans Circ Syst I, 2018, 65: 4336–4348

  17. 17

    Du H B, Li S H, Qian C J. Finite-time attitude tracking control of spacecraft with application to attitude synchronization. IEEE Trans Automat Contr, 2011, 56: 2711–2717

  18. 18

    Andrieu V, Praly L, Astolfi A. Homogeneous approximation, recursive observer design, and output feedback. SIAM J Control Opt, 2008, 47: 1814–1850

  19. 19

    Polyakov A. Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Automat Contr, 2012, 57: 2106–2110

  20. 20

    Parsegov S E, Polyakov A E, Shcherbakov P S. Fixed-time consensus algorithm for multi-agent systems with integrator dynamics. IFAC Proc Vol, 2013, 46: 110–115

  21. 21

    Zuo Z Y, Tie L. A new class of finite-time nonlinear consensus protocols for multi-agent systems. Int J Control, 2014, 87: 363–370

  22. 22

    Hong H F, Yu W W, Wen G H, et al. Distributed robust fixed-time consensus for nonlinear and disturbed multiagent systems. IEEE Trans Syst Man Cybern Syst, 2017, 47: 1464–1473

  23. 23

    Wang H, Yu W W, Wen G H, et al. Fixed-time consensus of nonlinear multi-agent systems with general directed topologies. IEEE Trans Circ Syst II Exp Briefs, in press. doi. https://doi.org/10.1109/TCSII.2018.2886298

  24. 24

    Zuo Z Y. Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica, 2015, 54: 305–309

  25. 25

    Fu J, Wang J Z. Fixed-time coordinated tracking for second-order multi-agent systems with bounded input uncertainties. Syst Control Lett, 2016, 93: 1–12

  26. 26

    Hong H F, Yu W W, Fu J J, et al. A novel class of distributed fixed-time consensus protocols for second-order nonlinear and disturbed multi-agent systems. IEEE Trans Netw Sci Eng, in press. doi:https://doi.org/10.1109/TNSE.2018.2873060

  27. 27

    Tian B L, Zuo Z Y, Wang H. Leader-follower fixed-time consensus of multi-agent systems with high-order integrator dynamics. Int J Control, 2017, 90: 1420–1427

  28. 28

    Ji M, Egerstedt M. Distributed coordination control of multiagent systems while preserving connectedness. IEEE Trans Robot, 2007, 23: 693–703

  29. 29

    Dimarogonas D V, Johansson K H. Decentralized connectivity maintenance in mobile networks with bounded inputs. In: Proceedings of IEEE International Conference on Robotics and Automation, Pasadena, 2008. 1507–1512

  30. 30

    Gustavi T, Dimarogonas D V, Egerstedt M, et al. Sufficient conditions for connectivity maintenance and rendezvous in leader-follower networks. Automatica, 2010, 46: 133–139

  31. 31

    Su H S, Wang X F, Chen G R. Rendezvous of multiple mobile agents with preserved network connectivity. Syst Control Lett, 2010, 59: 313–322

  32. 32

    Feng Z, Sun C, Hu G Q. Robust connectivity preserving rendezvous of multirobot systems under unknown dynamics and disturbances. IEEE Trans Control Netw Syst, 2017, 4: 725–735

  33. 33

    Cao Y C, Ren W, Casbeer D W, et al. Finite-time connectivity-preserving consensus of networked nonlinear agents with unknown Lipschitz terms. IEEE Trans Automat Contr, 2016, 61: 1700–1705

  34. 34

    Dong J G. Finite-time connectivity preservation rendezvous with disturbance rejection. Automatica, 2016, 71: 57–61

  35. 35

    Hong H F, Yu W W, Fu J J, et al. Finite-time connectivity-preserving consensus for second-order nonlinear multi-agent systems. IEEE Trans Control Netw Syst, in press. doi. https://doi.org/10.1109/TCNS.2018.2808599

  36. 36

    Tian B L, Lu H C, Zuo Z Y, et al. Fixed-time leader-follower output feedback consensus for second-order multiagent systems. IEEE Trans Cybern, in press. doi. https://doi.org/10.1109/TCYB.2018.2794759

  37. 37

    Zheng Y S, Zhu Y R, Wang L. Finite-time consensus of multiple second-order dynamic agents without velocity measurements. Int J Syst Sci, 2014, 45: 579–588

  38. 38

    Filippov A F. Differential Equations With Discontinuous Right-Hand Side, Mathematics and Its Applications (Soviet Series). Boston: Kluwer, 1988

  39. 39

    Bhat S P, Bernstein D S. Finite time stability of homogeneous systems. In: Proceedings of the 1997 American Control Conference, Albuquerque, 1997. 2513–2514

  40. 40

    Ren W, Beard R W. Distributed Consensus in Multi-Vehicle Cooperative Control. London: Springer-Verlag, 2008

  41. 41

    Rouche N, Habets P, Laloy M. Stability Theory by Liapunov’s Direct Method. New York: Springer-Verlag, 1977

  42. 42

    Alvarez J, Orlov I, Acho L. An invariance principle for discontinuous dynamic systems with application to a coulomb friction oscillator. J Dyn Sys Meas Control, 2000, 122: 687–690

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 61673107), National Ten Thousand Talent Program for Young Top-notch Talents (Grant No. W2070082), Cheung Kong Scholars Programme of China for Young Scholars (Grant No. Q2016109), Jiangsu Provincial Key Laboratory of Networked Collective Intelligence (Grant No. BM2017002), and Scientific Research Foundation of Graduate School of Southeast University (Grant No. YBJJ1718).

Author information

Correspondence to Wenwu Yu.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hong, H., Wang, H., Wang, Z. et al. Finite-time and fixed-time consensus problems for second-order multi-agent systems with reduced state information. Sci. China Inf. Sci. 62, 212201 (2019). https://doi.org/10.1007/s11432-018-9846-y

Download citation

Keywords

  • MASs
  • finite-time consensus
  • fixed-time consensus
  • connectivity-preserving mechanism
  • reduced state information