Skip to main content
SpringerLink
Log in

Fixed-Time Anti-Disturbance Average-Tracking for Multi-Agent Systems Without Velocity Measurements

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

In this paper, the authors tackle a fixed-time average-tracking problem for multi-agent systems which do not require velocity measurements and are affected by external mismatched and matched disturbances. The objective requires the considered agents with second-order dynamics to follow the average value of several time-varying reference signals, each of which is acquired by only one agent. First of all, the average value is estimated by using a novel distributed average estimator in a fixed time. Second, an original observer is created to provide estimated values in a fixed time for external mismatched and matched disturbances as well as unmeasured velocities of agents. Then, the authors propose a novel fixed-time anti-disturbance average-tracking protocol with the aid of the observer and a sliding mode surface. In the end, the feasibility of theoretical analysis is illustrated by some simulation experiments.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ekanayake S W and Pathirana P N, Smart cluster bombs-control of multi-agent systems for military applications, Proceedings of 2007 IEEE International Conference on Networking, Sensing and Control, London, 2007.

  2. Chen H L, Agricultural supply chain traceability system based on multi-agent system, Asian Agricultural Research, 2011, 3(10): 42–45, 49.

    MathSciNet  Google Scholar 

  3. Miftah E, Sayouti A, and Medromi H, Multi-agent systems and its application to control vehicle underwater, International Journal of Applied Information Systems, 2015, 9(7): 29–38.

    Article  Google Scholar 

  4. Liu C L and Liu F, Stationary consensus of heterogeneous multi-agent systems with bounded communication delays, Automatica, 2011, 47(9): 2130–2133.

    Article  MathSciNet  Google Scholar 

  5. Yang H Y, Guo L, and Zou H L, Robust consensus of multi-agent systems with time-delays and exogenous disturbances, International Journal of Control, Automation and Systems, 2012, 10(4): 797–805.

    Article  Google Scholar 

  6. Briñón-Arranz L, Seuret A, and Canudas-de-Wit C, Cooperative control design for time-varying formations of multi-agent systems, IEEE Transactions on Automatic Control, 2014, 59(8): 2283–2288.

    Article  MathSciNet  Google Scholar 

  7. Movric K H and Lewis F L, Cooperative optimal control for multi-agent systems on directed graph topologies, IEEE Transactions on Automatic Control, 2014, 59(3): 769–774.

    Article  MathSciNet  Google Scholar 

  8. Liu C L, Shan L, Chen Y Y, et al., Average-consensus filter of first-order multi-agent systems with disturbances, IEEE Transactions on Circuits and Systems II: Express Briefs, 2017, 65(11): 1763–1767.

    Google Scholar 

  9. Ghapani S, Rahili S, and Ren W, Distributed average tracking for second-order agents with nonlinear dynamics, Proceedings of 2016 American Control Conference (ACC), Boston, 2016.

  10. Zhao Y, Liu Y F, Li Z K, et al., Distributed average tracking for multiple signals generated by linear dynamical systems: An edge-based framework, Automatica, 2017, 75: 158–166.

    Article  MathSciNet  Google Scholar 

  11. Zhao Y, Liu Y F, Wen G H, et al., Distributed average tracking for lipschitz-type of nonlinear dynamical systems, IEEE Transactions on Cybernetics, 2018, 49(12): 4140–4152.

    Article  Google Scholar 

  12. Chen F, Cao Y C, and Ren W, Distributed average tracking of multiple time-varying reference signals with bounded derivatives, IEEE Transactions on Automatic Control, 2012, 57(12): 3169–3174.

    Article  MathSciNet  Google Scholar 

  13. Chen F, Ren W, Lan W Y, et al., Distributed average tracking for reference signals with bounded accelerations, IEEE Transactions on Automatic Control, 2015, 60(3): 863–869.

    Article  MathSciNet  Google Scholar 

  14. Ghapani S, Rahili S, and Ren W, Distributed average tracking of physical second-order agents with heterogeneous unknown nonlinear dynamics without constraint on input signals, IEEE Transactions on Automatic Control, 2018, 64(3): 1178–1184.

    Article  MathSciNet  Google Scholar 

  15. Liu C L, Shan L, Zhang Y, et al., Hierarchical average-tracking algorithm for multi-agent systems with unmatched constant references signals, IEEE Transactions on Circuits and Systems II: Express Briefs, 2020, 67(11): 2642–2646.

    Google Scholar 

  16. Liu C L, Li H, and Shan L, Stationary average-tracking problem of unmatched constant reference signals based on delayed-state feedback, International Journal of Systems Science, 2021, 52(13): 2725–2734.

    Article  MathSciNet  Google Scholar 

  17. Zhao Y, Liu Y F, Wen G H, et al., Finite-time distributed average tracking for second-order nonlinear systems, IEEE Transactions on Neural Networks and Learning Systems, 2019, 30(6): 1780–1789.

    Article  MathSciNet  Google Scholar 

  18. Hong H F, Wen G H, Yu X H, et al., Robust distributed average tracking for disturbed second-order multi-agent systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2022, 52(5): 3187–3199.

    Article  Google Scholar 

  19. Andrieu V, Praly L, and Astolfi A, Homogeneous approximation, recursive observer design, and output feedback, SIAM Journal on Control and Optimization, 2008, 47(4): 1814–1850.

    Article  MathSciNet  Google Scholar 

  20. Polyakov A, Nonlinear feedback design for fixed-time stabilization of linear control systems, IEEE Transactions on Automatic Control, 2012, 57(8): 2106–2110.

    Article  MathSciNet  Google Scholar 

  21. Hong H F, Yu W W, Yu X H, et al., Fixed-time connectivity-preserving distributed average tracking for multi-agent systems, IEEE Transactions on Circuits and Systems II: Express Briefs, 2017, 64(10): 1192–1196.

    Google Scholar 

  22. Chen Q, Shi G Q, Zhao Y, et al., Design fixed-time practical distributed average tracking algorithms for nonlinear signals with bounded-and lipschitz-type derivatives, IEEE Transactions on Circuits and Systems II: Express Briefs, 2020, 67(12): 3103–3107.

    Google Scholar 

  23. Wen G H, Yu X H, Fu J J, et al., Fast distributed average tracking in multi-agent networks: The case with general linear agent dynamics, IEEE Transactions on Control of Network Systems, 2021, 8(2): 997–1009.

    Article  MathSciNet  Google Scholar 

  24. Ghapani S, Ren W, Chen F, et al., Distributed average tracking for double-integrator multi-agent systems with reduced requirement on velocity measurements, Automatica, 2017, 81: 1–7.

    Article  MathSciNet  Google Scholar 

  25. Ding Y, Ren W, and Zhao Y, Robust distributed average tracking for double-integrator agents without velocity measurements under event-triggered communication, IEEE Transactions on Control of Network Systems, 2017, 8(2): 828–837.

    Article  MathSciNet  Google Scholar 

  26. Wang X Y, Li S H, and Lam J, Distributed active anti-disturbance output consensus algorithms for higher-order multi-agent systems with mismatched disturbances, Automatica, 2016, 74: 30–37.

    Article  MathSciNet  Google Scholar 

  27. Wang X Y, Li S H, Yu X H, et al., Distributed active anti-disturbance consensus for leader-follower higher-order multi-agent systems with mismatched disturbances, IEEE Transactions on Automatic Control, 2017, 62(11): 5795–5801.

    Article  MathSciNet  Google Scholar 

  28. Jin T, Liu Z W, Zhou H, et al., Scale-based cluster formation for multi-agent systems with mismatched disturbances, Journal of the Franklin Institute, 2019, 356(13): 7393–7410.

    Article  MathSciNet  Google Scholar 

  29. Ren W and Beard R W, Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE Transactions on Automatic Control, 2005, 50(5): 655–661.

    Article  MathSciNet  Google Scholar 

  30. Zuo Z Y and Tie L, A new class of finite-time nonlinear consensus protocols for multi-agent systems, International Journal of Control, 2014, 87(2): 363–370.

    Article  MathSciNet  Google Scholar 

  31. Bhat S P and Bernstein D S, Geometric homogeneity with applications to finite-time stability, Mathematics of Control, Signals and Systems, 2005, 17(2): 101–127.

    Article  MathSciNet  Google Scholar 

  32. Basin M, Rodriguez-Ramirez P, and Garza-Alonso A, Continuous fixed-time convergent super-twisting algorithm in case of unknown state and disturbance initial conditions, Asian Journal of Control, 2019, 21(1): 323–338.

    Article  MathSciNet  Google Scholar 

  33. Zuo Z Y, Nonsingular fixed-time consensus tracking for second-order multi-agent networks, Automatica, 2015, 54(9): 1833–1843.

    MathSciNet  Google Scholar 

  34. Li Y L, Liu C L, Zhang Y, et al., Distributed fixed-time average-tracking for multi-agent systems with mismatched and matched disturbances, Transactions of the Institute of Measurement and Control, 2022, 44(12): 2323–2335.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, Jiangnan University, Wuxi, 214122, China

    Yuling Li & Chenglin Liu

  2. School of Automation, Southeast University, Nanjing, 210096, China

    Ya Zhang & Yangyang Chen

Authors
  1. Yuling Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chenglin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ya Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yangyang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chenglin Liu.

Ethics declarations

The authors declare no conflict of interest.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 61973139, 61973082 and 61473138, and the Fundamental Research Funds for the Central Universities under Grant No. JUSRP22014.

This paper was recommended for publication by Editor DONG Yi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Y., Liu, C., Zhang, Y. et al. Fixed-Time Anti-Disturbance Average-Tracking for Multi-Agent Systems Without Velocity Measurements. J Syst Sci Complex 37, 985–1002 (2024). https://doi.org/10.1007/s11424-023-2461-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-023-2461-9

Keywords

Search

Navigation