Skip to main content

Observer-based self-triggered control for time-varying formation of multi-agent systems

Abstract

This paper studies the time-varying formation problem of general multi-agent systems with undirected topology via observer-based event-triggered control schemes. The distributed event-triggered control scheme and self-triggered control scheme are developed respectively. Each agent updates its next event time using current information without continuous communication in self-triggered control strategy. Formation error and state estimation error are considered simultaneously to get more accurate formation. Meanwhile, it is only when a request is received that each agent broadcasts its information. It is demonstrated that the time-varying formation can be achieved asymptotically under the two proposed control schemes and Zeno behavior can be excluded. Finally, numerical examples are provided to illustrate the effectiveness of the proposed observer-based event-triggered control strategies.

This is a preview of subscription content, access via your institution.

References

  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  Google Scholar 

  2. 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

    Article  Google Scholar 

  3. Jin Z W, Hu Y Y, Sun C Y. Event-triggered information fusion for networked systems with missing measurements and correlated noises. Neurocomputing, 2019, 332: 15–28

    Article  Google Scholar 

  4. Dong X W, Yu B S, Shi Z Y, et al. Time-varying formation control for unmanned aerial vehicles: theories and applications. IEEE Trans Control Syst Technol, 2015, 23: 340–348

    Article  Google Scholar 

  5. Zhang H, Feng G, Chen Q J, et al. Consensus of multi-agent systems with linear dynamics using event-triggered control. IET Control Theory Appl, 2014, 57: 2275–2281

    MathSciNet  Article  Google Scholar 

  6. Wang Q, Yu Y, Sun C Y. Distributed event-based consensus control of multi-agent system with matching nonlinear uncertainties. Neurocomputing, 2018, 272: 694–702

    Article  Google Scholar 

  7. Li Z K, Ren W, Liu X D, et al. Distributed containment control of multi-agent systems with general linear dynamics in the presence of multiple leaders. Int J Robust Nonlinear Control, 2013, 23: 534–547

    MathSciNet  Article  Google Scholar 

  8. Consolini L, Morbidi F, Prattichizzo D, et al. Leader-follower formation control of nonholonomic mobile robots with input constraints. Automatica, 2008, 44: 1343–1349

    MathSciNet  Article  Google Scholar 

  9. Lewis M A, Tan K H. High precision formation control of mobile robots using virtual structures. Auton Robot, 1997, 4: 387–403

    Article  Google Scholar 

  10. Balch T, Arkin R C. Behavior-based formation control for multirobot teams. IEEE Trans Robot Autom, 1998, 14: 926–939

    Article  Google Scholar 

  11. Das A K, Fierro R, Kumar V, et al. A vision-based formation control framework. IEEE Trans Robot Autom, 2002, 18: 813–825

    Article  Google Scholar 

  12. Oh K K, Park M C, Ahn H S. A survey of multi-agent formation control. Automatica, 2015, 53: 424–440

    MathSciNet  Article  Google Scholar 

  13. Cai D H, Zou H G, Wang J Z, et al. Event-triggered attitude tracking for rigid spacecraft. Sci China Inf Sci, 2019, 62: 222202

    MathSciNet  Article  Google Scholar 

  14. Dimarogonas D V, Frazzoli E, Johansson K H. Distributed event-triggered control for multi-agent systems. IEEE Trans Autom Control, 2012, 57: 1291–1297

    MathSciNet  Article  Google Scholar 

  15. Ding L, Han Q L, Ge X H, et al. An overview of recent advances in event-triggered consensus of multiagent systems. IEEE Trans Cybern, 2018, 48: 1110–1123

    Article  Google Scholar 

  16. Weng S X, Yue D. Distributed event-triggered cooperative attitude control of multiple rigid bodies with leader-follower architecture. Int J Syst Sci, 2016, 47: 631–643

    MathSciNet  Article  Google Scholar 

  17. Wang W, Huang C, Cao J D, et al. Event-triggered control for sampled-data cluster formation of multi-agent systems. Neurocomputing, 2017, 267: 25–35

    Article  Google Scholar 

  18. Tang T, Liu Z X, Chen Z Q. Event-triggered formation control of multi-agent systems. In: Proceedings of the 30th Chinese Control Conference, Yantai, 2011. 4783–4786

  19. Yi X L, Wei J Q, Dimarogonas D, et al. Formation control for multi-agent systems with connectivity preservation and event-triggered controllers. In: Proceedings of the 20th World Congress of the International-Federation-of-Automatic-Control (IFAC), Toulouse, 2017. 50: 9367–9373

    Google Scholar 

  20. Guo G, Ding L, Han Q L. A distributed event-triggered transmission strategy for sampled-data consensus of multi-agent systems. Automatica, 2014, 50: 1489–1496

    MathSciNet  Article  Google Scholar 

  21. Liu J, Zhang Y L, Yu Y, et al. Fixed-time event-triggered consensus for nonlinear multiagent systems without continuous communications. IEEE Trans Syst Man Cybern Syst, 2019, 49: 2221–2229

    Article  Google Scholar 

  22. Liu J, Zhang Y L, Sun C Y, et al. Fixed-time consensus of multi-agent systems with input delay and uncertain disturbances via event-triggered control. Inf Sci, 2019, 480: 261–272

    MathSciNet  Article  Google Scholar 

  23. Ge X H, Han Q L. Distributed formation control of networked multi-agent systems using a dynamic event-triggered communication mechanism. IEEE Trans Ind Electron, 2017, 64: 8118–8127

    Article  Google Scholar 

  24. Li X D, Dong X W, Li Q D, et al. Event-triggered time-varying formation control for general linear multi-agent systems. J Franklin Inst, 2019, 356: 10179–10195

    MathSciNet  Article  Google Scholar 

  25. Chu X, Peng Z X, Wen G G, et al. Distributed formation tracking of multi-robot systems with nonholonomic constraint via event-triggered approach. Neurocomputing, 2018, 275: 121–131

    Article  Google Scholar 

  26. Sun N, Fang Y C, Zhang X B. Energy coupling output feedback control of 4-DOF underactuated cranes with saturated inputs. Automatica, 2013, 49: 1318–1325

    MathSciNet  Article  Google Scholar 

  27. Zhang H, Feng G, Yan H C, et al. Observer-based output feedback event-triggered control for consensus of multi-agent systems. IEEE Trans Ind Electron, 2014, 61: 4885–4894

    Article  Google Scholar 

  28. Yu H, Antsaklis P J. Output synchronization of networked passive systems with event-driven communication. IEEE Trans Autom Control, 2014, 59: 750–756

    MathSciNet  Article  Google Scholar 

  29. Biggs N. Algebraic Graph Theory. Cambridge: Cambridge University Press, 1993

    MATH  Google Scholar 

  30. Dong X W, Shi Z Y, Lu G, et al. Time-varying output formation control for high-order linear time-invariant swarm systems. Inf Sci, 2015, 298: 36–52

    MathSciNet  Article  Google Scholar 

  31. Dong X W. Formation and Containment Control for High-order Linear Swarm Systems. Berlin: Springer, 2015

    Google Scholar 

  32. 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  Google Scholar 

  33. Kucera V. A contribution to matrix quadratic equations. IEEE Trans Autom Control, 1972, 17: 344–347

    MathSciNet  Article  Google Scholar 

  34. Chen Z Y, Han Q L, Yan Y M, et al. How often should one update control and estimation: review of networked triggering techniques. Sci China Inf Sci, 2020, 63: 150201

    MathSciNet  Article  Google Scholar 

  35. Xu Y, Wu Z G. Distributed adaptive event-triggered fault-tolerant synchronization for multi-agent systems. IEEE Trans Ind Electron, 2021, 68: 1537–1547

    Article  Google Scholar 

  36. Xu Y, Fang M, Wu Z G, et al. Input-based event-triggering consensus of multiagent systems under denial-of-service attacks. IEEE Trans Syst Man Cybern Syst, 2020, 50: 1455–1464

    Article  Google Scholar 

  37. Liu J, Zhang Y L, Liu H, et al. Robust event-triggered control of second-order disturbed leader-follower MASs: a nonsingular finite-time consensus approach. Int J Robust Nonlinear Control, 2019, 29: 4298–4314

    MathSciNet  Article  Google Scholar 

  38. Liu J, Zhang Y L, Yu Y, et al. Fixed-time leader-follower consensus of networked nonlinear systems via event/self-triggered control. IEEE Trans Neural Netw Learn Syst, 2020, 31: 5029–5037

    MathSciNet  Article  Google Scholar 

Download references

Acknowledgements

This work was partially supported by Fundamental Research Funds for the Central Universities (Grant No. FRF-GF-17-B46), National Natural Science Foundation of China (Grant Nos. 61703037, 61921004), and National Postdoctoral Program for Innovative Talents (Grant No. BX20200081). The authors would like to thank the anonymous associate editor and reviewers for their comments and suggestions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yao Yu.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chai, X., Liu, J., Yu, Y. et al. Observer-based self-triggered control for time-varying formation of multi-agent systems. Sci. China Inf. Sci. 64, 132205 (2021). https://doi.org/10.1007/s11432-019-2815-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-019-2815-7

Keywords

  • multi-agent systems
  • time-varying formation
  • states observer
  • event-triggered