Skip to main content
SpringerLink
Log in

Consensus in nonlinear multi-agent systems with nonidentical nodes and sampled-data control

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

This paper primarily discusses the leader-following consensus problem in nonlinear second-order multi-agent systems with nonidentical nodes. Sampled-data-based protocols are applied to reach consensus. Both delay-free and input-delay protocols are proposed. Based on the Lyapunov functional approach and linear matrix inequality (LMI) method, sufficient criteria are obtained to guarantee quasi-consensus for nonlinear heterogeneous multi-agent systems. All the heterogeneous followers can track the leader within a bounded range. Furthermore, the error systems between the leader and each follower eventually converge to a convergence domain that depends on the heterogeneity among the dynamics of the agents. Additionally, leader-following consensus can also be reached as the heterogeneity vanishes. Finally, numerical simulations are provided to illustrate the theoretical results.

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. He W L, Qian F, Lam J, et al. Quasi-synchronization of heterogeneous dynamic networks via distributed impulsive control: error estimation, optimization and design. Automatica, 2015, 62: 249–262

    MathSciNet  MATH  Google Scholar 

  2. Liu X Y, Cao J D, Yu W W, et al. Nonsmooth finite-time synchronization of switched coupled neural networks. IEEE Trans Cybern, 2016, 46: 2360–2371

    Google Scholar 

  3. Cao J D, Li R X. Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci China Inf Sci, 2017, 60: 032201

    Google Scholar 

  4. Li Q B, Guo J, Wu Y Y, et al. Global asymptotical bounded synchronization for a class of coupled complex networks with nonidentical nodes. Asian J Control, 2017, 19: 1630–1640

    MathSciNet  MATH  Google Scholar 

  5. Wang Z X, Jiang G P, Yu W W, et al. Synchronization of coupled heterogeneous complex networks. J Franklin Inst, 2017, 354: 4102–4125

    MathSciNet  MATH  Google Scholar 

  6. Ji M, Ferrari-Trecate G, Egerstedt M, et al. Containment control in mobile networks. IEEE Trans Autom Control, 2008, 53: 1972–1975

    MathSciNet  MATH  Google Scholar 

  7. Cao Y C, Ren W, Egerstedt M. Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks. Automatica, 2012, 48: 1586–1597

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  9. Su H S, Wang X F, Lin Z L. Flocking of multi-agents with a virtual leader. IEEE Trans Autom Control, 2009, 54: 293–307

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  11. Yu W W, Chen G R, Cao M, et al. Delay-induced consensus and quasi-consensus in multi-agent dynamical systems. IEEE Trans Circ Syst I, 2013, 60: 2679–2687

    MathSciNet  Google Scholar 

  12. Song Q, Cao J D, Yu W W. Second-order leader-following consensus of nonlinear multi-agent systems via pinning control. Syst Control Lett, 2010, 59: 553–562

    MathSciNet  MATH  Google Scholar 

  13. 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  MATH  Google Scholar 

  14. Wang Z, Cao J D. Quasi-consensus of second-order leader-following multi-agent systems. IET Control Theory Appl, 2012, 6: 545–551

    MathSciNet  Google Scholar 

  15. Cai H, Huang J. Leader-following adaptive consensus of multiple uncertain rigid spacecraft systems. Sci China Inf Sci, 2016, 59: 010201

    Google Scholar 

  16. Jadbabaie A, Lin J, Morse A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control, 2003, 48: 988–1001

    MathSciNet  MATH  Google Scholar 

  17. Ding L, Zheng W X. Consensus tracking in heterogeneous nonlinear multi-agent networks with asynchronous sampleddata communication. Syst Control Lett, 2016, 96: 151–157

    MATH  Google Scholar 

  18. Lin P, Jia Y M. Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies. Automatica, 2009, 45: 2154–2158

    MathSciNet  MATH  Google Scholar 

  19. 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  MATH  Google Scholar 

  20. 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  MATH  Google Scholar 

  21. 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  MATH  Google Scholar 

  22. Liu X Y, Ho D W C, Cao J D, et al. Discontinuous observers design for finite-time consensus of multiagent systems with external disturbances. IEEE Trans Neural Netw Learn Syst, 2017, 28: 2826–2830

    MathSciNet  Google Scholar 

  23. Wang Z H, Zhang H S, Fu M Y, et al. Consensus for high-order multi-agent systems with communication delay. Sci China Inf Sci, 2017, 60: 092204

    MathSciNet  Google Scholar 

  24. Tian Y P, Zhang Y. High-order consensus of heterogeneous multi-agent systems with unknown communication delays. Automatica, 2012, 48: 1205–1212

    MathSciNet  MATH  Google Scholar 

  25. Chen F, Chen Z Q, Xiang L Y, et al. Reaching a consensus via pinning control. Automatica, 2009, 45: 1215–1220

    MathSciNet  MATH  Google Scholar 

  26. Liu X W, Chen T P, Lu W L. Consensus problem in directed networks of multi-agents via nonlinear protocols. Phys Lett A, 2009, 373: 3122–3127

    MathSciNet  MATH  Google Scholar 

  27. 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

    Google Scholar 

  28. He W L, Qian F, Han Q L, et al. Synchronization error estimation and controller design for delayed Lur’e systems with parameter mismatches. IEEE Trans Neural Netw Learn Syst, 2012, 23: 1551–1563

    Google Scholar 

  29. Su H S, Qiu Y, Wang L. Semi-global output consensus of discrete-time multi-agent systems with input saturation and external disturbances. ISA Trans, 2017, 67: 131–139

    Google Scholar 

  30. Zhang W B, Tang Y, Wu X T, et al. Synchronization of nonlinear dynamical networks with heterogeneous impulses. IEEE Trans Circ Syst I, 2014, 61: 1220–1228

    Google Scholar 

  31. Hu J Q, Liang J L, Cao J D. Synchronization of hybrid-coupled heterogeneous networks: pinning control and impulsive control schemes. J Franklin Inst, 2014, 351: 2600–2622

    MathSciNet  MATH  Google Scholar 

  32. 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  MATH  Google Scholar 

  33. Yu W W, Zhou L, Yu X H, et al. Consensus in multi-agent systems with second-order dynamics and sampled data. IEEE Trans Ind Inf, 2013, 9: 2137–2146

    Google Scholar 

  34. Gao Y P, Wang L. Sampled-data based consensus of continuous-time multi-agent systems with time-varying topology. IEEE Trans Autom Control, 2011, 56: 1226–1231

    MathSciNet  MATH  Google Scholar 

  35. Yu W W, Zheng W X, Chen G R, et al. Second-order consensus in multi-agent dynamical systems with sampled position data. Automatica, 2011, 47: 1496–1503

    MathSciNet  MATH  Google Scholar 

  36. Zhang W B, Tang Y, Huang T W, et al. Sampled-data consensus of linear multi-agent systems with packet losses. IEEE Trans Neural Netw Learn Syst, 2017, 28: 2516–2527

    MathSciNet  Google Scholar 

  37. He W L, Zhang B, Han Q L, et al. Leader-following consensus of nonlinear multiagent systems with stochastic sampling. IEEE Trans Cybern, 2016, 47: 327–338

    Google Scholar 

  38. Wen G H, Duan Z S, Yu W W, et al. Consensus of multi-agent systems with nonlinear dynamics and sampled-data information: a delayed-input approach. Int J Robust Nonlinear Control, 2013, 23: 602–619

    MathSciNet  MATH  Google Scholar 

  39. Huang N, Duan Z S, Chen G R. Some necessary and sufficient conditions for consensus of second-order multi-agent systems with sampled position data. Automatica, 2016, 63: 148–155

    MathSciNet  MATH  Google Scholar 

  40. Wan Y, Cao J D, Alsaedi A, et al. Distributed observer-based stabilization of nonlinear multi-agent systems with sampled-data control. Asian J Control, 2017, 19: 918–928

    MathSciNet  MATH  Google Scholar 

  41. Wang L, Chen S Y, Wang Q G. Eigenvalue based approach to bounded synchronization of asymmetrically coupled networks. Commun Nonlinear Sci Numer Simul, 2015, 22: 769–779

    MathSciNet  MATH  Google Scholar 

  42. Park P G, Ko JW, Jeong C. Reciprocally convex approach to stability of systems with time-varying delays. Automatica, 2011, 47: 235–238

    MathSciNet  MATH  Google Scholar 

  43. Fridman E, Dambrine M. Control under quantization, saturation and delay: an LMI approach. Automatica, 2009, 45: 2258–2264

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was jointly supported by National Natural Science Foundation of China (Grant Nos. 61304169, 61573096, 61573194), Natural Science Foundation of Jiangsu Province of China (Grant No. BK20181387), and Natural Science Foundation of the Higher Education Institutions of Jiangsu Province of China (Grant No. 17KJD110006). The authors would like to express their sincere appreciation to the associate editor and the anonymous reviewers for their helpful comments and suggestions.

Author information

Authors and Affiliations

  1. School of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China

    Zhengxin Wang & Jingbo Fan

  2. School of Automation, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China

    Guo-Ping Jiang & Min Xiao

  3. Research Center for Complex Systems and Network Sciences, School of Mathematics, Southeast University, Nanjing, 210096, China

    Jinde Cao

  4. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Ahmed Alsaedi

Authors
  1. Zhengxin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jingbo Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guo-Ping Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jinde Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Min Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ahmed Alsaedi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jinde Cao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Z., Fan, J., Jiang, GP. et al. Consensus in nonlinear multi-agent systems with nonidentical nodes and sampled-data control. Sci. China Inf. Sci. 61, 122203 (2018). https://doi.org/10.1007/s11432-018-9441-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-018-9441-4

Keywords

Search

Navigation