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Consensus of delayed multi-agent dynamical systems with stochastic perturbation via impulsive approach

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Abstract

In the article, the topic of consensus for delayed multi-agent dynamical systems with stochastic perturbation and impulsive effects is investigated. By introducing the stochastic and impulsive disturbances effects which are omnipresent not only in manmade systems but also in nature into the multi-agent systems, our control scheme is much more reasonable in real systems. Both internal delay and transmission delay are all under consideration in our paper. Based on the algebraic graph theory, the Lyapunov stability theory and Halanay inequality matrix theory, some adequate conditions are proposed to guarantee the consensus of delayed multi-agent dynamical systems with stochastic perturbation via impulsive control. The pinning control is also presented in the paper. Simulation results are given to verify the validity of the proposed control mechanism finally.

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References

  1. Cao J, Li H, Ho DWC (2005) Synchronization criteria of Lur’e systems with time-delay feedback control. Chaos, Solitons & Fractals 23:1285–1298

    Article  MathSciNet  MATH  Google Scholar 

  2. Cao Y, Yu W, Ren W et al (2013) An overview of recent progress in the study of distributed multi-agent coordination. IEEE Trans Ind Inform 9:427–438

    Article  Google Scholar 

  3. Friedman A (1975) Stochastic differential equations and applications. Academic Press, New York

    MATH  Google Scholar 

  4. He W, Chen G et al (2015) Network-based leader-following consensus of nonlinear multi-agent systems via distributed impulsive control. Inf Sci

  5. Hu M, Guo L, Hu A (2015) Leader-following consensus of linear multi-agent systems with randomly occurring nonlinearities and uncertainties and stochastic disturbances. Neurocomputing 149:884890

    Article  Google Scholar 

  6. Hu J, Wang Z et al (2012) Robust sliding mode control for discrete stochastic systems with mixed time delays, randomly occuring uncertainties and randomly occurring nonlinearities. IEEE Trans Ind Electron 59:3008–3015

    Article  Google Scholar 

  7. Kao Y, Xie J et al (2015) A slide mode approach to \(H_{\infty }\) non-fragile oberserver-based control design for uncertain Markovian neural-type stochastic systems. Automatica 52:218–225

    Article  MATH  Google Scholar 

  8. Kin H, Shim H et al (2011) Output consensus of heterogeneous uncertain linear multi-agent systems. IEEE Trans Autom Control 56:200–206

    Article  MathSciNet  MATH  Google Scholar 

  9. Li C, Yu W, Huang T (2014) Impulsive synchronization schemes of stochastic complex networks with switching topology: average time approach. Neural Netw 54:85–94

    Article  MATH  Google Scholar 

  10. Li H, Liao X, Huang T, Zhu W (2015) Event-triggering sampling based leader-following consensus in second-order multi-agent systems. IEEE Trans Autom Control 60:1998–2003

    Article  MathSciNet  MATH  Google Scholar 

  11. Li C, Yu X, Yu W, Huang T, Liu Z (2015) Distributed event-triggered scheme for economic dispatch in smart grids. IEEE Trans Ind Inform. doi:10.1109/TII.2015.2479558

    Google Scholar 

  12. Li C, Yu X, Huang T, Chen G, He X (2016) A generalized Hopfield network for nonsmooth constrained convex optimization: Lie derivative approach. IEEE Trans Neural Netw Learn Syst 27:308–321

    Article  MathSciNet  Google Scholar 

  13. Li C, Yu X, Yu W, Chen G, Wang J (2016) Efficient computation for sparse load shifting in demand side management. IEEE Trans Smart Grid. doi:10.1109/TSG.2016.2521377

    Google Scholar 

  14. Liu B, Lu W, Chen T (2013) Pinning consensus in networks of multiagents via a single impulsive controller. IEEE Trans Netw Learn Syst 24:1141–1149

    Article  Google Scholar 

  15. Lu JQ, Ding CD, Lou JG, Cao JD (2015) Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers. J Frankl Inst 352:5024–5041

    Article  MathSciNet  Google Scholar 

  16. Ma T et al (2015) Impulsive consensus of multi-agent nonlinear systems with control gain error. Neurocomputing 171:293–298

    Article  Google Scholar 

  17. Ma T (2015) Synchronization of muti-agent stochastic impulsive pertubed chaotic delayed neural networks with switching topology. Neurocomputing 151:1392–1406

    Article  Google Scholar 

  18. Senthikuma T, Balsubramaniam P (2011) Delay-dependent robust stabilization and \(H_{\infty }\) control for nonlinear stochastic system switch Markovian jump parameters and interval time-varying delays. J Optim Theory Appl 151:100–120

    Article  MathSciNet  Google Scholar 

  19. Sun YG, Wang L, Xie GM (2012) Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays. Syst Control 22(14):1571–1582

    Google Scholar 

  20. Tan C, Liu G, Shi P (2015) Consensus of networked multi-agent systems with diverse time-varying communication delays. J Frankl Inst. doi:10.1016/j.jfranklin.2015.04.002

    Google Scholar 

  21. Wang Y, Wang Z, Liang J (2009) Global synchronization for delayed complex netwroks with randomly occurring nonlinearities and multiple stochastic disturbances. J Phys A Math Theor 42:135101

    Article  MATH  Google Scholar 

  22. Wang Z, Wang Y, Liu Y (2010) Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mix time delays. IEEE Trans Neural Netw 21:11–25

    Article  Google Scholar 

  23. Wang Y, Cao J (2013) Cluster synchronization in nonlinearly coupled delayed networks of non-identical dynamic systems. Nonlinear Anal Real World Appl 14(1):2107–2115

    MathSciNet  MATH  Google Scholar 

  24. Wang W, Zhang W et al (2013) Stochastic synchronization of complex networks with mixed impulses. IEEE Trans Circuits Syst I Regual 60:2657–2667

    Article  MathSciNet  Google Scholar 

  25. Wen G, Duan Z, Yu W et al (2013) Consensus of second-order multi-agent systems with delayed nonlinear dynamics and intermittent communications. Int J Control 86(2):322–331

    Article  MathSciNet  MATH  Google Scholar 

  26. Xie D, Liang T (2015) Second-order group consensus for multi-agent systems with time delays. Neurocomputing 153:133–139

    Article  Google Scholar 

  27. Yang H, Zhang Z et al (2011) Consensus of second-order multi-agent systems with exoogenous distrubances. Int J Robust Nonlinear Control 21(9):945–956

    Article  Google Scholar 

  28. Zhang H, Ma T, Huang G, Wang Z (2010) Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control. IEEE Trans Syst Cybern B 40:831–844

    Article  Google Scholar 

  29. Zhang W, Li C, Huang T, Xiao M (2015) Synchronization of complex networks with stochastic perturbation via aperiodically intermittent control. Neural Netw 71:105–111

    Article  Google Scholar 

  30. Zhang X, Liu X (2013) Further results on consenus of second-order multi-agent systems with exogenous distrubance. IEEE Trans Circuits Syst I60(12):3215–3226

    Article  Google Scholar 

  31. Zhao L, Jia Y (2015) Finite-time consensus for second-order stochastic multi-agent systems with nonlinear dynamics. Appl Math Comput 270:278–290

    MathSciNet  Google Scholar 

  32. Zong GD, Yang D, Hou LL, Wang QZ (2013) Robust finite-time \(H_\infty\) control for Markovian jump systems with partially known transition probabilities. J Frankl Inst 350(6):1562–1578

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors are grateful to the anonymous reviewers for their valuable comments and suggestions that have helped to improve the prostration of the paper. This work was supported in part by the National Natural Science Foundation of China under Grant 61472331, in part by the Research Fund of Preferential Development Domain for the Doctoral Program of Ministry of Education of China under Grant 201101911130005, in part by the Fundamental Research Funds for the Central Universities under Grant XDJK2014C117, in part by the Innovation Foundation for Postgraduate of Chongqing University under Grant CDJXS12180011 and in part by the Natural Science Foundation of China under Grant 61403314.

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Authors and Affiliations

  1. College of Computer Science, Chongqing University, Chongqing, 400044, People’s Republic of China

    Shasha Yang & Xiaofeng Liao

  2. College of Computer Science, Chongqing University of Posts and Telecommunications, Chongqing, 400044, People’s Republic of China

    Yanbing Liu

  3. School of Software Engineering, Chongqing University, Chongqing, 400044, People’s Republic of China

    Xin Chen

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  1. Shasha Yang
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  2. Xiaofeng Liao
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  3. Yanbing Liu
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  4. Xin Chen
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Correspondence to Shasha Yang.

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Yang, S., Liao, X., Liu, Y. et al. Consensus of delayed multi-agent dynamical systems with stochastic perturbation via impulsive approach. Neural Comput & Applic 28 (Suppl 1), 647–657 (2017). https://doi.org/10.1007/s00521-016-2393-6

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  • DOI: https://doi.org/10.1007/s00521-016-2393-6

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