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Journal of Systems Science and Complexity

, Volume 32, Issue 2, pp 588–599 | Cite as

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

  • Li Qiu
  • Liuxiao GuoEmail author
  • Jia Liu
Article
  • 32 Downloads

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.

Keywords

Mean square average generalized consensus multi-agent systems stochastic disturbances time delays 

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References

  1. [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.CrossRefGoogle Scholar
  2. [2]
    Olfati-Saber R, Flocking for multi-agent dynamic systems: Algorithms and theory, IEEE Transaction on Automatic Control, 2006, 51(3): 401–420.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Ren W, Multi-vehicle consensus with a time-varying reference state, Systems and Control Letters, 2007, 56(7): 474–483.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [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.CrossRefGoogle Scholar
  8. [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.CrossRefGoogle Scholar
  9. [9]
    Ma Z, Liu Z, and Chen Z, Leader-following consensus of multi-agent system with a smart leader, Neurocomputing, 2016, 214: 401–408.CrossRefGoogle Scholar
  10. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [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.CrossRefGoogle Scholar
  12. [12]
    Pecora L M and Carroll T L, Synchronization in chaotic systems, Physical Review Letters, 1990, 64(8): 821–824.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Kadir A, Wang X Y, and Zhao Y Z, Generalized synchronization of diverse structure chaotic systems, Chinese Physics Letters, 2011, 28(9): 090503.CrossRefGoogle Scholar
  16. [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.CrossRefGoogle Scholar
  17. [17]
    Sun W and Li S, Generalized outer synchronization between two uncertain dynamical networks, Nonlinear Dynamics, 2014, 77(3): 481–489.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [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. [19]
    Martinez-Guerra R and Mata-Machuca J L, Generalized synchronization via the differential primitive element, Applied Mathematics and Computation, 2014, 232: 848–857.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [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.CrossRefGoogle Scholar
  21. [21]
    Liu J, Liu X, and Xie WC, Stochastic consensus seeking with communication delays, Automatica, 2011, 47(12): 2689–2696.Google Scholar
  22. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [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.MathSciNetCrossRefGoogle Scholar
  25. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    Horn R A and Johnson C R, Matrix Analysis, Cambridge University, UK, 1985.CrossRefzbMATHGoogle Scholar
  27. [27]
    Xia Y Q, Fu M Y, and Shi P, Analysis and Synthesis of Dynamical Systems with Time-Delays, Springer-Verlag, New York, 2011.zbMATHGoogle Scholar
  28. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [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

Copyright information

© The Editorial Office of JSSC & Springer-Verlag GmbH Germany 2019

Authors and Affiliations

  1. 1.School of ScienceJiangnan UniversityWuxiChina

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