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Cognitive Neurodynamics

, Volume 13, Issue 4, pp 367–377 | Cite as

Consensus of uncertain multi-agent systems with input delay and disturbances

  • L. Susana Ramya
  • R. SakthivelEmail author
  • Yong Ren
  • Yongdo Lim
  • A. Leelamani
Research Article
  • 104 Downloads

Abstract

In this paper, the problem of robust consensus for multi-agent systems affected by external disturbances is discussed. A novel consensus control is developed by using a feedback controller based on disturbance rejection and Smith predictor scheme. Specifically, the disturbance rejection performance of the uncertain multi-agent systems is improved according to the estimation of equivalent-input-disturbance and the effect of time delay in the control system is reduced via Smith predictor scheme by shifting the delay outside the feedback loop. Furthermore, by combining Lyapunov theory, matrix inequality techniques and properties of Kronecker product, a robust feedback controller for each agent is designed such that the desired consensus of the uncertain multi-agent systems affected by external disturbances can be ensured. Finally, to illustrate the validity of the designed control scheme, two numerical examples with simulation results are provided.

Keywords

Multi-agent systems Consensus Equivalent-input-disturbance Smith predictor 

Notes

Acknowledgements

The work of L. Susana Ramya was supported by Department of Science & Technology, Government of India through Women Scientists Scheme-A under grant no. SR/WOS-A/PM-101/2016.

References

  1. Astrom KJ, Hang CC, Lim BC (1994) A new Smith predictor for controlling a process with an integrator and long dead-time. IEEE Trans Autom Control 39:343–355CrossRefGoogle Scholar
  2. Gao F, Wu M, She J, Cao W (2016) Disturbance rejection in nonlinear systems based on equivalent-input-disturbance approach. Appl Math Comput 282:244–253Google Scholar
  3. Gao F, Wu M, She J, He Y (2016) Delay-dependent guaranteed-cost control based on combination of Smith predictor and equivalent-input-disturbance approach. ISA Trans 62:215–221CrossRefGoogle Scholar
  4. Hou W, Fu MY, Zhang H (2016) Consensusability of linear multiagent systems with time delay. Int J Robust Nonlinear Control 26:2529–2541CrossRefGoogle Scholar
  5. Lee D, Lee M, Sung S, Lee I (1999) Robust PID tuning for smith predictor in the presence of model uncertainty. J Process Control 9:79–85CrossRefGoogle Scholar
  6. Lin H, Su H, Shu Z, Wu ZG, Xu Y (2016) Optimal estimation in UDP-like networked control systems with intermittent inputs: stability analysis and suboptimal filter design. IEEE Trans Autom Control 61:1794–1809CrossRefGoogle Scholar
  7. Lin H, Su H, Chen MZQ, Shu Z, Lu R, Wua ZG (2018) On stability and convergence of optimal estimation for networked control systems with dual packet losses without acknowledgment. Automatica 90:81–90CrossRefGoogle Scholar
  8. Liu RJ, Liu GP, Wu M, Xiao FC, She J (2014) Robust disturbance rejection based on the equivalent-input-disturbance approach. Syst Control Lett 70:100–108CrossRefGoogle Scholar
  9. Liu RJ, Liu GP, Wu M, Nie ZY (2014) Disturbance rejection for time-delay systems based on the equivalent-input-disturbance approach. J Frankl Inst 351:3364–3377CrossRefGoogle Scholar
  10. Liu H, Karimi HR, Du S, Xia W, Zhong C (2017) Leader-following consensus of discrete-time multiagent systems with time-varying delay based on large delay theory. Inf Sci 417:236–246CrossRefGoogle Scholar
  11. Murray RM (2007) Recent research in cooperative control of multivehicle systems. J Dyn Syst Meas Control 129:571–583CrossRefGoogle Scholar
  12. Namerikawa T, Yoshioka C (2008) Consensus control of observer-based multi-agent system with communication delay. In: SICE annual conference.  https://doi.org/10.1109/SICE.2008.4655069
  13. Ou M, Du H, Li S (2012) Robust consensus of second-order multi-agent systems with input and time-varying communication delays. Int J Modell Identif Control 17:284–294CrossRefGoogle Scholar
  14. Revathi VM, Balasubramaniam P, Ratnavelu K (2016) Delay-dependent \(H_\infty\) filtering for complex dynamical networks with time-varying delays in nonlinear function and network couplings. Signal Process 118:122–132CrossRefGoogle Scholar
  15. Sakthivel R, Mohanapriya S, Selvaraj P, Karimi HR, Marshal Anthoni S (2017) EID estimator-based modified repetitive control for singular systems with time-varying delay. Nonlinear Dyn 354:3813–3837Google Scholar
  16. Sakthivel R, Sakthivel R, Kaviarasan B, Alzahrani F (2018) Leader-following exponential consensus of input saturated stochastic multi-agent systems with Markov jump parameters. Neurocomputing 287:84–92CrossRefGoogle Scholar
  17. She J, Fang M, Ohyama Y, Hashimoto H, Wu M (2008) Improving disturbance-rejection performance based on an equivalent-input disturbance approach. IEEE Trans Ind Electron 555:380–389CrossRefGoogle Scholar
  18. Shi CX, Yang GH (2018) Robust consensus control for a class of multi-agent systems via distributed PID algorithm and weighted edge dynamics. Appl Math Comput 316:73–88Google Scholar
  19. Smith OJ (1959) A controller to overcome dead time. ISA Trans 6:28–33Google Scholar
  20. Sun F, Zhu W, Li Y, Liu F (2016) Finite-time consensus problem of multi-agent systems with disturbance. J Frankl Inst 353:2576–2587CrossRefGoogle Scholar
  21. Szalkai B, Kerepesi C, Varga B, Grolmusz V (2017) Parameterizable consensus connectomes from the Human Connectome Project: the Budapest Reference Connectome Server v3.0. Cogn Neurodyn 11:113–116CrossRefGoogle Scholar
  22. Tian X, Liu H, Liu H (2018) Robust finite-time consensus control for multi-agent systems with disturbances and unknown velocities. ISA Trans 80:73–80CrossRefGoogle Scholar
  23. Ursino M, Cuppini C, Cappa SF, Catricala E (2018) A feature-based neurocomputational model of semantic memory. Cogn Neurodyn 12:525–547CrossRefGoogle Scholar
  24. Wang Q, Yu Y, Sun C (2018) Distributed event-based consensus control of multi-agent system with matching nonlinear uncertainties. Neurocomputing 272:694–702CrossRefGoogle Scholar
  25. Wu Y, Su H, Shi P, Shu Z, Wu ZG (2016) Consensus of multiagent systems using aperiodic sampled-data control. IEEE Trans Cybern 46:2132–2143CrossRefGoogle Scholar
  26. Xi J, Yu Y, Liu G, Zhong Y (2014) Guaranteed-cost consensus for singular multi-agent systems with switching topologies. IEEE Trans Circuits Syst I Reg Pap 61:1531–1542CrossRefGoogle Scholar
  27. Zhang X, Liu X (2018) Containment of linear multi-agent systems with disturbances generated by heterogeneous nonlinear exosystems. Neurocomputing 315:283–291CrossRefGoogle Scholar
  28. Zhang W, Tang Y, Huang T, Kurths J (2016) Sampled-data consensus of linear multi-agent systems with packet losses. IEEE Trans Neural Netw Learn Syst 28:2516–2527CrossRefGoogle Scholar
  29. Zhang F, Duan S, Wang L (2017) Route searching based on neural networks and heuristic reinforcement learning. Cogn Neurodyn 11:245–258CrossRefGoogle Scholar
  30. Zhao L, Jia Y, Yu J, Du J (2017) \(H_\infty\) sliding mode based scaled consensus control for linear multi-agent systems with disturbances. Appl Math Comput 292:375–389Google Scholar
  31. Zhu F, Wang R, Pan X, Zhu Z (2018) Energy expenditure computation of a single bursting neuron. Cogn Neurodyn 23:1–13Google Scholar
  32. Zuo Z, Wang C, Ding Z (2016) Robust consensus control of uncertain multi-agent systems with input delay: a model reduction method. Int J Robust Nonlinear Control 10:1–20Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • L. Susana Ramya
    • 1
  • R. Sakthivel
    • 2
    Email author
  • Yong Ren
    • 3
  • Yongdo Lim
    • 4
  • A. Leelamani
    • 1
  1. 1.Department of MathematicsAnna University Regional CampusCoimbatoreIndia
  2. 2.Department of Applied MathematicsBharathiar UniversityCoimbatoreIndia
  3. 3.Department of MathematicsAnhui Normal UniversityWuhuChina
  4. 4.Department of MathematicsSungkyunkwan UniversitySuwonSouth Korea

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