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Mean Square Average Generalized Consensus of Multi-Agent Systems Under Time-Delays and Stochastic Disturbances

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Abstract

Compared with the traditional consensus problem, this paper deals with the mean square average generalized consensus (MSAGC) of multi-agent systems under fixed directed topology, where all agents are affected by stochastic disturbances. Distributed protocol depending on delayed time information from neighbors is designed. Based on Lyapunov stability theory, together with results from matrix theory and Itô's derivation theory, the linear matrix inequalities approach is used to establish sufficient conditions to ensure MSAGC of multi-agent systems. Finally, numerical simulations are provided to illustrate the theoretical results.

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References

  1. Chen Y and Lu J, Multi-agent systems with dynamical topologies: Consensus and applications, IEEE Circuits and System Magazine, 2013, 48(6): 21–34.

    Article  Google Scholar 

  2. Olfati-Saber R, Flocking for multi-agent dynamic systems: Algorithms and theory, IEEE Transaction on Automatic Control, 2006, 51(3): 401–420.

    Article  MathSciNet  MATH  Google Scholar 

  3. Tanner H, Jadbabaie A, and Pappas G J, Flocking in fixed and switching networks, IEEE Transaction on Automatic Control, 2007, 52(5): 863–868.

    Article  MathSciNet  MATH  Google Scholar 

  4. Ren W, Multi-vehicle consensus with a time-varying reference state, Systems and Control Letters, 2007, 56(7): 474–483.

    Article  MathSciNet  MATH  Google Scholar 

  5. Li T and Zhang J F, Mean square average-consensus under measurement noises and fixed topologies: Necessary and sufficient conditions, Automatica, 2009, 45(8): 1929–1936.

    Article  MathSciNet  MATH  Google Scholar 

  6. Ni Y H and Li X, Consensus seeking in multi-agent systems with multiplicative measurement noises, Systems and Control Letters, 2013, 62(5): 430–437.

    Article  MathSciNet  MATH  Google Scholar 

  7. Liu J, Guo L X, and Hu M F, Distributed delay control of multi-agent systems with nonlinear dynamics: Stochastic disturbance, Neurocomputing, 2015, 152: 164–169.

    Article  Google Scholar 

  8. Hu M F, Guo L X, Hu A H, et al., Leader-following consensus of linear multi-agent systems with randomly occurring noonlinearities and uncertainties and stochastic disturbances, Neurocomputing, 2015, 149: 884–890.

    Article  Google Scholar 

  9. Ma Z, Liu Z, and Chen Z, Leader-following consensus of multi-agent system with a smart leader, Neurocomputing, 2016, 214: 401–408.

    Article  Google Scholar 

  10. Liu Z W, Guan Z H, Li T, et al., Quantized consensus of multi-agent systems via broadcast gossip algorithms, Asian Journal of Control, 2012, 14(6): 1634–1642.

    Article  MathSciNet  MATH  Google Scholar 

  11. Han Y, Lu W, and Chen T, Cluster consensus in discrete-time networks of multi-agents with inter-cluster nonidentical inputs, IEEE Transactions on Neural Networks and Learning Systems, 2013, 24(4): 566–578.

    Article  Google Scholar 

  12. Pecora L M and Carroll T L, Synchronization in chaotic systems, Physical Review Letters, 1990, 64(8): 821–824.

    Article  MathSciNet  MATH  Google Scholar 

  13. Hu A H, Xu Z Y, and Guo L X, The existence of generalized synchronization of chaotic systems in complex networks, Chaos: An Interdisciplinary Journal of Nonlinear Science, 2010, 20(1): 013112.

    Article  MathSciNet  MATH  Google Scholar 

  14. Yuan Z L, Xu Z Y, and Guo L X, Generalized synchronization of two bidirectionally coupled discrete dynamical systems, Communications in Nonlinear Science and Numerical Simulation, 2012, 17(2): 992–1002.

    Article  MathSciNet  MATH  Google Scholar 

  15. Kadir A, Wang X Y, and Zhao Y Z, Generalized synchronization of diverse structure chaotic systems, Chinese Physics Letters, 2011, 28(9): 090503.

    Article  Google Scholar 

  16. Guan S, Wang X, and Gong X, The development of generalized synchronization on complex networks, Chaos: An Interdisciplinary Journal of Nonlinear Science, 2009, 19(1): 013130.

    Article  Google Scholar 

  17. Sun W and Li S, Generalized outer synchronization between two uncertain dynamical networks, Nonlinear Dynamics, 2014, 77(3): 481–489.

    Article  MathSciNet  MATH  Google Scholar 

  18. Ouannas A and Odibat Z, Generalized synchronization of different dimensional chaotic dynamical systems in discrete time, Nonlinear Dynamics, 2015, 81(1–2): 765–771.

    Google Scholar 

  19. Martinez-Guerra R and Mata-Machuca J L, Generalized synchronization via the differential primitive element, Applied Mathematics and Computation, 2014, 232: 848–857.

    Article  MathSciNet  MATH  Google Scholar 

  20. Guo L X, Hu M F, Hu A H, et al., Linear and nonlinear generalized consensus of multi-agent system, Chinese Physics B, 2014, 23(5): 050508.

    Article  Google Scholar 

  21. Liu J, Liu X, and Xie WC, Stochastic consensus seeking with communication delays, Automatica, 2011, 47(12): 2689–2696.

    Google Scholar 

  22. Olfati-Saber R and Murray R M, Consensus problems in networks of agents with switching topology and time-delays, IEEE Transaction on Automatic Control, 2004, 49(9): 1520–1533.

    Article  MathSciNet  MATH  Google Scholar 

  23. Yang H, Zhang Z, and Zhang S, Consensus of second-order multi-agent systems with exogenous disturbance, International Journal of Robust and Nonlinear Control, 2011, 21(9): 945–956.

    Article  MathSciNet  MATH  Google Scholar 

  24. Zhang X and Liu X, Further results on consensus of second-order multi-agent systems with exogenous disturbance, IEEE Transaction on Circuits and System I: Regular papers, 2013, 60(12): 3215–3226.

    Article  MathSciNet  Google Scholar 

  25. Wen G, Duan Z, and Yu W, Consensus of multi-agent systems with nonlinear dynamics and sampled-data information, International Journal of Robust and Nonlinear Control, 2013, 23(6): 602–619.

    Article  MathSciNet  MATH  Google Scholar 

  26. Horn R A and Johnson C R, Matrix Analysis, Cambridge University, UK, 1985.

    Book  MATH  Google Scholar 

  27. Xia Y Q, Fu M Y, and Shi P, Analysis and Synthesis of Dynamical Systems with Time-Delays, Springer-Verlag, New York, 2011.

    MATH  Google Scholar 

  28. Wang Y, Wang Z, and Liang J, Global synchronization for delayed complex networks with randomly occuring nonlinearities and multiple stochastic disturbances, Journal of Physics A: Mathematical and Theoretical, 2009, 42(13): 135101.

    Article  MathSciNet  MATH  Google Scholar 

  29. Gu K Q, An intergral inequality in the stability problem of time-delay systems, Proceeding of the 39th IEEE Conference Decision and Control, 2000, 2805–2810.

    Google Scholar 

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Authors and Affiliations

  1. School of Science, Jiangnan University, Wuxi, 214122, China

    Li Qiu, Liuxiao Guo & Jia Liu

Authors
  1. Li Qiu
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  2. Liuxiao Guo
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  3. Jia Liu
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Corresponding author

Correspondence to Liuxiao Guo.

Additional information

This research was supported by the Natural Science Foundation of Jiangsu Province under Grant No. BK2016 1126 and the Prospective Research Project of Jiangsu Province under Grant No. BY2016022-17.

This paper was recommended for publication by Editor LIU Guoping.

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Qiu, L., Guo, L. & Liu, J. Mean Square Average Generalized Consensus of Multi-Agent Systems Under Time-Delays and Stochastic Disturbances. J Syst Sci Complex 32, 588–599 (2019). https://doi.org/10.1007/s11424-018-7107-y

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  • DOI: https://doi.org/10.1007/s11424-018-7107-y

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