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Finite-Time and Fixed-Time Synchronization of Complex Networks with Discontinuous Nodes via Quantized Control

  • Wanli Zhang
  • Shiju Yang
  • Chuandong LiEmail author
  • Zunbin Li
Article
  • 20 Downloads

Abstract

This paper investigates finite-time (FET) and fixed-time (FDT) synchronization of discontinuous complex networks (CNs) via quantized controllers. These control schemes can take full advantage of limited communication resources. By designing Lyapunov function and using different control schemes, several sufficient conditions are proposed such that the dynamical CNs are able to realize synchronization within a settling time. The settling time is related to the initial values of the considered systems using FET control, while it is regardless of the initial values when a special case of FET control named FDT control is utilized. Moreover, FET and FDT synchronization of discontinuous CNs are also considered via some existing controllers without logarithmic quantization, respectively. Numerical simulations are presented to demonstrate the theoretical results.

Keywords

Finite-time synchronization Fixed-time synchronization Complex networks Quantized control 

Notes

Acknowledgements

This work was jointly supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. 61374078, 61673078, 61633011.

References

  1. 1.
    Stogatz SH, Stewart I (1993) Coupled oscillators and biological synchronization. Sci Am 269(6):102–109CrossRefGoogle Scholar
  2. 2.
    Xie Q, Chen G, Bollt EM (2002) Hybrid chaos synchronization and its application in information processing. Math Comput Model 35(1):145–163MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Li C, Liao X, Wong K (2005) Lag synchronization of hyperchaos with application to secure communications. Chaos Solitons Fractals 23(1):183–193MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Li C, Chen G (2004) Synchronization in general complex dynamical networks with coupling delays. Phys A 343:263–278MathSciNetCrossRefGoogle Scholar
  5. 5.
    Huang T, Li C, Duan S, Starzyk J (2012) Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects. IEEE Trans Neural Netw Learn Syst 23:866–875CrossRefGoogle Scholar
  6. 6.
    Li X, Rakkiyappan R (2013) Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays. Commun Nonlinear Sci Numer Simul 18(6):1515–1523MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Li C, Yu W, Huang T (2014) Impulsive synchronization schemes of stochastic complex networks with switching topology: average time approach. Neural Netw 54:85–94CrossRefzbMATHGoogle Scholar
  8. 8.
    Vincent UE, Guo R (2011) Finite-time synchronization for a class of chaotic and hyperchaotic systems via adaptive feedback controller. Phys Lett A 375:2322–2326CrossRefzbMATHGoogle Scholar
  9. 9.
    Aghababa MP, Khanmohammadi S, Alizadeh G (2011) Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. Appl Math Model 35(6):3080–3091MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Haimo VT (1986) Finite-time controllers. SIAM J Control Optim 24(4):760–770MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Bowong S, Kakmeni F (2003) Chaos control and duration time of a class of uncertain chaotic systems. Phys Lett A 316:206–217CrossRefzbMATHGoogle Scholar
  12. 12.
    Aghababa MP, Aghababa HP (2012) Synchronization of mechanical horizontal platform systems in finite time. Appl Math Model 36(10):4579–4591MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Yang X, Wu Z, Cao J (2013) Finite-time synchronization of complex networks with nonidentical discontinuous nodes. Nonlinear Dyn 73(4):2313–2327MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Zhou C, Zhang W, Yang X, Xu C, Feng J (2017) Finite-time synchronization of complex-valued neural networks with mixed delays and uncertain perturbations. Neural Process Lett 46:271–291CrossRefGoogle Scholar
  15. 15.
    Polyakov A (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Yang X, Lam J, Ho DWC, Feng Z (2017) Fixed-time synchronization of complex networks with impulsive effects via nonchattering control. IEEE Trans Autom Control 62(11):5511–5521MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Zhang W, Li C, Huang T, Huang J (2018) Fixed-time synchronization of complex networks with nonidentical nodes and stochastic noise perturbations. Phys. A 492:1531–1542MathSciNetCrossRefGoogle Scholar
  18. 18.
    Polyakov A, Efimov D, Perruquetti W (2015) Finite-time and fixedtime stabilization: implicit Lyapunov function approach. Automatica 51:332–340MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Zuo Z, Tie L (2016) Distributed robust finite-time nonlinear consensus protocols for multi-agent systems. Int J Syst Sci 47(6):1366–1375MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Cao J, Li R (2017) Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci China Inf Sci 60(3):032201MathSciNetCrossRefGoogle Scholar
  21. 21.
    Zhu X, Yang X, Alsaadi FE, Hayat T (2018) Fixed-time synchronization of coupled discontinuous neural networks with nonidentical perturbations. Neural Process Lett 48:1161–1174CrossRefGoogle Scholar
  22. 22.
    Lu W, Chen T (2008) Almost periodic dynamics of a class of delayed neural networks with discontinuous activations. Neural Comput 20(4):1065–1090MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Yang X, Cao J (2013) Exponential synchronization of delayed neural networks with discontinuous activations. IEEE Trans Circuits Syst 60(9):2431–2439MathSciNetCrossRefGoogle Scholar
  24. 24.
    Yang X, Ho DWC, Lu J, Song Q (2015) Finite-time cluster synchronization of T–S fuzzy complex networks with discontinuous subsystems and random coupling delays. IEEE Trans Fuzzy Syst 23(6):2302–2316CrossRefGoogle Scholar
  25. 25.
    Yang X, Song Q, Liang J, He B (2015) Finite-time synchronization of coupled discontinuous neural networks with mixed delays and nonidentical perturbations. J Frankl Inst 352(10):4382–4406MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Filippov AF (1988) Differential equations with discontinuous righthand sides. Kluwer Academic, DordrechtCrossRefGoogle Scholar
  27. 27.
    Forti M, Nistri P (2003) Global convergence of neural networks with discontinuous neuron activations. IEEE Trans Circuits Syst 50(11):1421–1435MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Forti M, Nistri P, Papini D (2005) Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Trans Neural Netw 16(6):1449–1463CrossRefGoogle Scholar
  29. 29.
    Zhang W, Yang X, Xu C, Feng J, Li C (2018) Finite-time synchronization of discontinuous neural networks with delays and mismatched parameters. IEEE Trans Neural Netw Learn Syst 29(8):3761–3771MathSciNetCrossRefGoogle Scholar
  30. 30.
    Ji G, Hu C, Yu J, Jiang H (2018) Finite-time and fixed-time synchronization of discontinuous complex networks: a unified control framework design. J Frankl Inst.  https://doi.org/10.1016/j.jfranklin.2018.04.026
  31. 31.
    Brockett RW, Liberzon D (2000) Quantized feedback stabilization of linear systems. IEEE Trans Autom Control 45(7):1279–1289MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Tian E, Yue D, Peng C (2008) Quantized output feedback control for networked control systems. Inf Sci 178(12):2734–2749MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Song G, Li T, Li Y, Lu J (2016) Quantized output feedback stabilization for nonlinear discrete-time systems subject to saturating actuator. Nonlinear Dyn 83(1):305–317MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Li H, Chen G, Huang T, Dong Z, Zhu W, Gao L (2016) Event-triggered distributed average consensus over directed digital networks with limited communication bandwidth. IEEE Trans Cybern 46:3098–3110CrossRefGoogle Scholar
  35. 35.
    Wan Y, Cao J, Wen G (2017) Quantized synchronization of chaotic neural networks with scheduled output feedback control. IEEE Trans Neural Netw Learn Syst 28(11):2638–2647MathSciNetCrossRefGoogle Scholar
  36. 36.
    Xu C, Yang X, Lu J, Feng J, Alsaadi FE, Hayat T (2017) Finte-time synchronization of networks via quantized intermittent pinning control. IEEE Trans Cybern.  https://doi.org/10.1109/TCYB.2017.2749248
  37. 37.
    Strogatz SH, Stewart I (1993) Coupled oscillators and biological synchronization. Sci Am 269(6):102–109CrossRefGoogle Scholar
  38. 38.
    Adamic LA, Huberman BA (1999) Growth dynamics of the world wide web. Nature 401(6749):131Google Scholar
  39. 39.
    Liu B, Lu W, Chen T (2012) New conditions on synchronization of networks of linearly coupled dynamical systems with non-Lipschitz right-hand sides. Neural Netw 25:5–13CrossRefzbMATHGoogle Scholar
  40. 40.
    Clarke FH (1987) Optimization and nonsmooth analysis. SIAM, PhiladelphiaGoogle Scholar
  41. 41.
    Hardy G, Littlewood J, Polya G (1952) Inequalities, 2nd edn. Cambridge University Press, CambridgezbMATHGoogle Scholar
  42. 42.
    Forti M, Grazzini M, Nistri P, Pancioni L (2006) Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations. Phys D 214(1):88–99MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Lu W, Liu X, Chen T (2016) A note on finite-time and fixedtime stability. Neural Netw 81:11–15CrossRefGoogle Scholar
  44. 44.
    Brown R (1993) Generalizations of the Chua equations. IEEE Trans Circuits Syst 40(11):878–884CrossRefzbMATHGoogle Scholar
  45. 45.
    Barabási AL, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509–512MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.National and Local Joint Engineering Laboratory of Intelligent Transmission and Control Technology (Chongqing), College of Electronic and Information EngineeringSouthwest UniversityChongqingChina

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