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Finite-Time Synchronization for a Class of Dynamical Complex Networks with Nonidentical Nodes and Uncertain Disturbance

  • Qingbo Li
  • Jin GuoEmail author
  • Changyin Sun
  • Yuanyuan Wu
  • Zhengtao Ding
Article
  • 17 Downloads

Abstract

This paper investigates the finite-time synchronization for a class of linearly coupled dynamical complex networks with both nonidentical nodes and uncertain disturbance. A set of controllers are designed such that the considered system can be finite-timely synchronized onto the target node. Based on the stability of the error equation, the Lyapunov function method and the linear matrix inequality technique, several sufficient conditions are derived to ensure the finite-time synchronization, and applied to the case of identical nodes and the one without uncertain disturbance. Also the adaptive finite-time synchronization is discussed. A numerical example is given to show the effectiveness of the main results obtained.

Keywords

Disturbance dynamical complex networks finite-time synchronization nonidentical nodes 

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References

  1. [1]
    Yu W, Chen G, and Lü J, On pinning synchronization of complex dynamical networks, Automatica, 2009, 45(2): 429–435.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Wu C W, Synchronization in Complex Networks of Nonlinear Dynamical Systems, World Scientific, Singapore, 2007.CrossRefzbMATHGoogle Scholar
  3. [3]
    Osipov G, Kurths J, and Zhou C, Synchronization in Oscillatory Networks, Springer, Berlin, 2007.CrossRefzbMATHGoogle Scholar
  4. [4]
    Arenas A, Daz-Guilera A, Kurths J, et al., Synchronization in complex networks, Physics Reports, 2008, 469: 93–153.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Song Q and Cao J D, On pinning synchronization of directed and undirected complex dynamical networks, IEEE Trans. Circuits Syst. I., 2010, 57: 672–680.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Wu Y Y, Cao J D, Alofic A, et al., Finite-time boundedness and stabilization of uncertain switched neural networks with time-varying delay, Neural Networks, 2015, 69: 135–143.CrossRefGoogle Scholar
  7. [7]
    Ma C and Zhang J, On formability of linear continuous multi-agent systems, Journal of Systems Science and Complexity, 2012, 25(1): 13–29.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Zhou J, Lu J, and Lü J, Pinning adaptive synchronization of a general complex dynamical network, Automatica, 2008, 44(4): 996–1003.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    Ding Z and Li Z, Distributed adaptive consensus control of nonlinear output-feedback systems on directed graphs, Automatica, 2016, 72: 46–52.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Xia W and Cao J, Pinning synchronization of delayed dynamical networks via periodically intermittent control, Chaos, 2009, 19: 113–120.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    Cai S M, Liu Z R, Xu F D, et al., Periodically intermittent controlling complex dynamcial networks with time-varying delays to a desired orbit, Phys. Lett. A, 2009, 373: 3846–3854.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Liu X and Chen T, Cluster synchronization in directed networks via intermittent pinning control, IEEE Transactions on Neural Networks, 2011, 22(7): 1009–1020.CrossRefGoogle Scholar
  13. [13]
    Li H, Hu C, Jiang H, et al., Synchronization of fractional-order complex dynamical networks via periodically intermittent pinning control, Chaos Solitons and Fractals, 2017, 103: 357–363.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    Zhang Q, Lu J, and Zhao J, Impulsive synchronization of general continuous and discrete-time complex dynamical networks, Commun. Nonlinear Sci. Numer. Simul., 2010, 15: 1063–1070.CrossRefzbMATHGoogle Scholar
  15. [15]
    Yang X, Cao J D, and Lu J Q, Synchronization of delayed complex dynamical networks with impulsive and stochastic effects, Nonlinear Anal. RWA, 2011, 12: 2252–2266.zbMATHGoogle Scholar
  16. [16]
    Gong X, Gan L, and Wu Z, Adaptive impulsive cluster synchronization in community network with nonidentical nodes, International Journal of Modern Physics C, 2016, 27(1): 1650010.MathSciNetCrossRefGoogle Scholar
  17. [17]
    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.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    Chen X Y, Park Ju H, Cao J D, et al., Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances, Applied Mathematics and Computation, 2017, 308: 161–173.MathSciNetCrossRefGoogle Scholar
  19. [19]
    Lü L, Yu M, Li C, et al., Projective synchronization of a class of complex network based on high-order sliding mode control, Nonlinear Dynamics, 2013, 73(1–2): 411–416.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Hou H, Zhang Q, and Zheng M, Cluster synchronization in nonlinear complex networks under sliding mode control, Nonlinear Dynamics, 2016, 83(12): 739–749.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    Wang Y W, Xiao J W, Wen C, et al., Synchronization of continuous dynamical networks with discrete-time communications, IEEE Trans. Neural Netw., 2011, 22(120): 1979–1986.CrossRefGoogle Scholar
  22. [22]
    Wu Z, Park J, Su H, et al., Exponential synchronization for complex dynamical networks with sampled-data, Journal Franklin I, 2012, 349(9): 2735–2749.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    Zhao J, Hill D, Liu T, et al., Stability of dynamical networks with nonidentical nodes: A multiple V-Lyapunov function method, Automatica, 2011, 47: 2615–2625.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    Song Q, Cao J D, and Liu F, Synchronization of complex dynamical networks with nonidentical nodes, Physics Letters A, 2010, 374(4): 544–551.CrossRefzbMATHGoogle Scholar
  25. [25]
    Wang S, Yao H, Zheng S, et al., A novel criterion for cluster synchronization of complex dynamical networks with coupling time-varying delays, Communications in Nonlinear Science and Numerical Simulation, 2012, 17(7): 2997–3004.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    Yang X, Wu Z, and Cao J, Finite-time synchronization of complex networks with nonidentical discontinuous nodes, Nonlinear Dynamics, 2013, 73(4): 2313–2327.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    Lu J Q, Ho D W, Cao J D, et al., Exponential synchronization of linearly coupled neural networks with impulsive disturbances, IEEE Trans Neural Netw., 2011, 22(2): 329–336.CrossRefGoogle Scholar
  28. [28]
    Cai G, Jiang S, Cai S, et al., Cluster synchronization of overlapping uncertain complex networks with time-varying impulse disturbances, Nonlinear Dynamics, 2015, 80(1–2): 503–513.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    Jiang S, Lu X, Cai G, et al., Adaptive fixed-time control for cluster synchronisation of coupled complex networks with uncertain disturbances, International Journal of Systems Science, 2017, 48(16): 1–9.MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    Ma C, Li T, and Zhang J, Consensus control for leader-following multi-agent systems with measurement noises, Journal of Systems Science and Complexity, 2010, 23(1): 35–49.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    Yang X and Cao J, Finite-time stochastic synchronization of complex networks, Appl. Math. Model, 2010, 34(11): 3631–3641.MathSciNetzbMATHGoogle Scholar
  32. [32]
    Chen Y G, Fei S M, and Li Y M, Robust stabilization for uncertain saturated time-delay systems: A distributed-delay-dependent polytopic approach, IEEE Transactions on Automatic Control, 2017, 62(7): 3455–3460.MathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    Zong G D, Ren H L, and Hou L L, Finite-time stability of interconnected impulsive switched systems, IET Control Theory and Applications, 2016, 10(6): 648–654.MathSciNetCrossRefGoogle Scholar
  34. [34]
    Zong G D, Wang R H, Zheng W X, et al., Finite-time H∞ control for discrete-time switched nonlinear systems with time delay, International Journal of Robust and Nonlinear Control, 2015, 25(6): 914–936.MathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    Langville A N and Stewart W J, The Kronecker product and stochastic automata networks, J. Comput. Appl. Math., 2004, 16(7): 429–447.zbMATHGoogle Scholar
  36. [36]
    Wan Y, Cao J D, Wen G H, et al., Robust fixed-time synchronization of delayed Cohen-Grossberg neural networks, Neural Networks, 2016, 73: 86–94.CrossRefzbMATHGoogle Scholar
  37. [37]
    Zhao J, Hill D J, and Liu T, Global bounded synchronization of general dynamical networks with nonidentical nodes, IEEE Transactions on Automatic Control, 2012, 57(10): 2656–2662.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Qingbo Li
    • 1
    • 2
  • Jin Guo
    • 1
    • 3
    Email author
  • Changyin Sun
    • 4
  • Yuanyuan Wu
    • 5
  • Zhengtao Ding
    • 6
  1. 1.School of Automation and Electrical EngineeringUniversity of Science and Technology BeijingBeijingChina
  2. 2.College of Mathematics and Information ScienceZhengzhou University of Light IndustryZhengzhouChina
  3. 3.Key Laboratory of Knowledge Automation for Industrial ProcessesMinistry of EducationBeijingChina
  4. 4.School of AutomationSoutheast UniversityNanjingChina
  5. 5.College of Electric and Information EngineeringZhengzhou University of Light IndustryZhengzhouChina
  6. 6.School of Electrical and Electronic EngineeringUniversity of ManchesterManchesterUK

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