Advertisement

Finite-time Synchronization Control Relationship Analysis of Two Classes of Markovian Switched Complex Networks

  • Xin Wang
  • Bin Yang
  • Kun Gao
  • Jian-an Fang
Regular Papers Control Theory and Applications
  • 30 Downloads

Abstract

In this paper, finite-time global synchronization control problem for a class of nonlinear coupling Markovian switched complex networks (NCMSCNs) is investigated. Furthermore, according to differentiability of nonlinear coupling function g(x,y), g(x,y) how to affect synchronization dynamics of the class of NCMSCNs is analyzed by two viewpoints. The first is that if g(x,y) satisfies the Lipschitz condition and is derivable, the above question is discussed by taking g(x,y) = L1x+L2y, g(x,y) =–L1x+L2y, g(x,y) = L1xL2y and g(x,y) =–L1xL2y, where L1 > 0, L2 > 0. The second is that if nonlinear coupling function g(x,y) only satisfies the Lipschitz condition, by analyzing the differences of synchronization control rules for the class of NCMSCNs and a class of linear coupling Markovian switched complex networks (LCMSCNs), the problem is explored. Comparing the previous works [12,21,22,26,33,34], the main improvement of this paper is that the works of this paper extend the existed analyzing ideas of the finite-time global synchronization for nonlinear coupling complex networks, including NCMSCNs.

Keywords

Control rules finite-time synchronization linear coupling nonlinear coupling synchronization control 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    D. J. Watts and S. H. Strogatz, “Collective dynamics of ‘small-world’ networks,” Nature, vol. 393, pp. 440–442, June 1998.CrossRefzbMATHGoogle Scholar
  2. [2]
    E. N. Sanchez, D. I. Rodriguez-Castellanos, G. R. Chen, and R. Ruiz-Cruz, “Pinning control of complex network synchronization: a recurrent neural network approach,” International Journal of Control, Automation, and Systems, vol. 15, no. 3, pp. 1405–1413, June 2017.CrossRefGoogle Scholar
  3. [3]
    Z. Tang, J. H. Park, and W. X. Zheng, “Distributed impulsive synchronization of Lur’e dynamical networks via parameter variation methods,” International Journal of Robust and Nonlinear Control, vol. 28, no. 3, pp. 1001–1015, January 2018.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    C. Ge, H. Wang, Y. J. Liu, and J. H. Park, “Further results on stabilization of neural-network based systems using sampled-data control,” Nonlinear Dynamics, vol. 90, no. 3, pp. 1–11, November 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Z. Tang, J. H. Park, and H. Shen, “Finite-time cluster synchronization of Lur’e networks: a nonsmooth approach,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 48, no. 8, pp. 1213–1224, August 2018.CrossRefGoogle Scholar
  6. [6]
    R. M. Zhang, D. Q. Zeng, J. H. Park, S. M. Zhong, and Y. B. Yu, “Novel discontinuous control for exponential synchronization of memristive recurrent neural networks with heterogeneous time-varying delays,” Journal of the Franklin Institute, vol. 355, no. 5, pp. 2826–2848, March 2018.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    Y. R. Liu, Z. D. Wang, L. F. Ma, Y. Cui, and F. E. Alsaadi, “Synchronization of directed switched complex networks with stochastic link perturbations and mixed time-delays,” Nonlinear Analysis: Hybrid Systems, vol. 27, pp. 213–224, February 2018.MathSciNetzbMATHGoogle Scholar
  8. [8]
    Z. Tang, J. H. Park, and J. W. Feng, “Novel approaches to pin cluster synchronization on complex dynamical networks in Lur’s forms,” Communications in Nonlinear Science and Numerical Simulation, vol. 57, pp. 422–438, April 2018.MathSciNetCrossRefGoogle Scholar
  9. [9]
    W. L. Zhang, X. S. Yang, C. Xu, J. W. Feng, and C. D. Li, “Finite-time synchronization of discontinuous neural networks with delays and mismatched parameters,” IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no.8, pp. 3761–3771, August 2018.Google Scholar
  10. [10]
    C. Ge, B. F. Wang, X. Wei, and Y. J. Liu, “Exponential synchronization of a class of neural networks with sampled-data control,” Applied Mathematics and Computation, vol. 315, pp. 150–161, December 2017.MathSciNetCrossRefGoogle Scholar
  11. [11]
    Z. G. Yan, Y. X. Song, and J. H. Park, “Quantitative mean square exponential stability and stabilization of stochastic systems with Markovian switching,” Journal of the Franklin Institute, vol. 355, no.8, pp. 3438–3454, May 2018.Google Scholar
  12. [12]
    H. L. Dong, J. M. Zhou, B. C. Wang, and M. Q. Xiao, “Synchronization of nonlinearly and stochastically coupled Markovian switching networks via event-triggered sampling,” IEEE Transactions on Neural Networks and Learning Systems, vol 29, no. 11, pp. 5691–5700, November 2018.CrossRefGoogle Scholar
  13. [13]
    H. L. Dong, D. F. Ye, J. W. Feng, and J. Y. Wang, “Almost sure cluster synchronization of Markovian switching complex networks with stochastic noise via decentralized adaptive pinning control,” Nonlinear Dynamics, vol. 87, no. 2, pp. 727–739, January 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    X. J. Huang and Y. C. Ma, “Finite-time H¥ sampled-data synchronization for Markovian jump complex networks with time-varying delays,” Neurocomputing, vol. 296, pp. 82–99, June 2018.CrossRefGoogle Scholar
  15. [15]
    J. M. Zhou, H. L. Dong, and J.W. Feng, “Event-triggered communication for synchronization of Markovian jump delayed complex networks with partially unknown transition rates,” Applied Mathematics and Computation, vol. 293, pp. 617–629, January 2017.MathSciNetCrossRefGoogle Scholar
  16. [16]
    K. Sivaranjani and R. Rakkiyappan, “Delayed impulsive synchronization of nonlinearly coupled Markovian jumping complex dynamical networks with stochastic perturbations,” Nonlinear Dynamics, vol. 88, no. 3, pp. 1917–1934, May 2017.CrossRefzbMATHGoogle Scholar
  17. [17]
    D. Q. Zeng, R. M. Zhang, S. M. Zhong, J. Wang, and K. B. Shi, “Sampled-data synchronization control for Markovian delayed complex dynamical networks via a novel convex optimization method,” Neurocomputing, vol. 266, pp. 606–618, November 2017.CrossRefGoogle Scholar
  18. [18]
    A. J. Wang, T. Dong, and X. F. Liao, “Event-triggered synchronization strategy for complex dynamical networks with the Markovian switching topologies,” Neural Networks, vol. 74, pp. 52–57, February 2016.CrossRefzbMATHGoogle Scholar
  19. [19]
    P. F. Wang, Y. Hong, and H. Su, “Stabilization of stochastic complex-valued coupled delayed systems with Markovian switching via periodically intermittent control,” Nonlinear Analysis: Hybrid Systems, vol. 29, pp. 395–413, August 2018.MathSciNetzbMATHGoogle Scholar
  20. [20]
    L. L. Li, Z. W. Tu, J. Mei, and J. G. Jian, “Finite-time synchronization of complex delayed networks via intermittent control with multiple switched periods,” Nonlinear Dynamics, vol. 85, pp. 375–388, July 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    X. Wang, J.-A. Fang, H. Y. Mao and A. D. Dai, “Finitetime global synchronization for a class of Markovian jump complex networks with partially unknown transition rates under feedback control,” Nonlinear Dynamics, vol. 79, no. 1, pp. 47–61, January 2015.CrossRefzbMATHGoogle Scholar
  22. [22]
    W. X. Cui, S. Y. Sun, J.-A Fang, Y. L. Xu, and L. D. Zhao, “Finite-time synchronization of Markovian jump complex networks with partially unknown transition rates,” Journal of The Franklin Institute, vol. 351, pp. 2543–2561, May 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    X. J. Li and G. H. Yang, “FLS-based adaptive synchronization control of complex dynamical networks with nonlinear couplings and state-dependent uncertainties,” IEEE Transactions on Cybernetics, vol. 46, no. 1, pp. 171–180, January 2016.CrossRefGoogle Scholar
  24. [24]
    C. Zhang, X. Y. Wang, C. Luo, J. Q. Li, and C. P. Wang, “Robust outer synchronization between two nonlinear complex networks with parametric disturbances and mixed time-varying delays,” Physica A: Statistical Mechanics and its Applications, vol. 494, pp. 251–264, March 2018.MathSciNetCrossRefGoogle Scholar
  25. [25]
    J. W. Feng, S. Y. Chen, J. Y. Wang, and Y. Zhao, “Quasisynchronization of coupled nonlinear memristive neural networks with time delays by pinning control,” IEEE Access, vol. 6, pp. 26271–26282, May 2018.CrossRefGoogle Scholar
  26. [26]
    X. W. Liu and T. P. Chen, “Synchronization of nonlinear coupled networks via aperiodically intermittent pinning control,” IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 1, pp. 113–126, January 2015.MathSciNetCrossRefGoogle Scholar
  27. [27]
    Y. F. Lei, L. L. Zhang, Y. H. Wang, and Y. Q. Fan, “Generalized matrix projective outer synchronization of non-dissipatively coupled time-varying complex dynamical networks with nonlinear coupling functions,” Neurocomputing, vol. 230, pp. 390–396, March 2017.CrossRefGoogle Scholar
  28. [28]
    X. Z. Jin, G. H. Yang, and W. W. Che, “Adaptive pinning control of deteriorated nonlinear coupling networks with circuit realization,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 9, pp. 1345–1355, September 2012.CrossRefGoogle Scholar
  29. [29]
    J. P. Tseng, “Global cluster synchronization in nonlinearly coupled community networks with heterogeneous coupling delays,” Neural Networks, vol. 86, pp. 18–31, February 2017.CrossRefGoogle Scholar
  30. [30]
    D. X. Peng, X. D. Li, C. Aouiti, and F. Miaadi, “Finitetime synchronization for Cohen-Grossberg neural networks with mixed time-delays,” Neurocomputing, vol. 294, pp. 39–47, June 2018.CrossRefGoogle Scholar
  31. [31]
    Z. Y. Guo, S. Q. Gong, and T.W. Huang, “Finite-time synchronization of inertial memristive neural networks with time delay via delay-dependent control,” Neurocomputing, vol. 293, pp. 100–107, June 2018.CrossRefGoogle Scholar
  32. [32]
    S. H. Qiu, Y. L. Huang, and S. Y. Ren, “Finite-time synchronization of multi-weighted complex dynamical networks with and without coupling delay,” Neurocomputing, vol. 275, pp. 1250–1260, January 2018.CrossRefGoogle Scholar
  33. [33]
    Q. Xie, G. Q. Si, Y. B. Zhang, Y. W. Yuan, and R. Yao, “Finite-time synchronization and identification of complex delayed networks with Markovian jumping parameters and stochastic perturbations,” Chaos, Solitons and Fractals, vol. 86, pp. 35–49, May 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    X. H. Liu, X. H. Yu, and H. S. Xi, “Finite-time synchronization of neutral complex networks with Markovian switching based on pinning controller,” Neurocomputing, vol. 153, pp. 148–158, April 2015.CrossRefGoogle Scholar
  35. [35]
    W. X. Cui, J.-A. Fang, W. B. Zhang and X. Wang, “Finitetime cluster synchronization of Markovian switching complex networks with stochastic perturbations,” IET Control Theory and Applications, vol. 8, no. 1, pp. 30–41, January 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    X. W. Liu and T. P. Chen, “Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix,” Physica A, vol. 387, pp. 4429–4439, July 2008.CrossRefGoogle Scholar
  37. [37]
    Y. Feng, F. L. Han and X. H. Yu, “Chattering free fullorder sliding-mode control,” Automatica, vol. 50, no.4, pp. 1310–1314, April 2014.Google Scholar
  38. [38]
    Y. Tang, “Terminal sliding mode control for rigid robots,” Automatica, vol. 34. no. 1, pp. 51–56, January 1998.Google Scholar
  39. [39]
    A. Saghafinia, H.W. Ping, M. N. Uddin, and K. S. Gaeid, “Adaptive fuzzy sliding-mode control into chattering-free IM drive,” IEEE Transactions on Industry Applications, vol. 51, no. 1, pp. 692–701, January-February 2015.CrossRefGoogle Scholar
  40. [40]
    J. L. Yin, S. Y. Khoo, Z. H. Man and X. H. Yu, “Finitetime stability and instability of stochastic nonlinear systems,” Automatica, vol. 47, pp. 2671–2677, December 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    S. P. Bhat and D. S. Bernstein, “Finite-time stability of continuous antonomous systems,” SIAM: SIAM Journal on Control and Optimization, vol. 38, no. 3, pp. 751–766, 2000.MathSciNetzbMATHGoogle Scholar
  42. [42]
    S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Philadelphia, SIAM, 1994.CrossRefzbMATHGoogle Scholar
  43. [43]
    J. Mei, M. H. Jiang, W. M. Xu, and B. Wang, “Finitetime synchronization control of complex dynamical networks with time delay,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, pp. 2462–2478, September 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    L. Wang and F. Xiao, “Finite-time consensus problems for networks of dynamic agents,” IEEE Transactions on Automatic Control, vol. 55, no. 4, pp. 950–955, February 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    L. O. Chua, M. Itoh, L. Kocarev, and K. Eckert, “Chaos synchronization in Chua’s circuit,” Journal of Circuits, Systems and Computers, vol. 3, no. 1, pp. 93–108, 1993.MathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    C. Ge, H. Wang, Y. J. Liu, and J. H. Park, “Improved stabilization criteria for fuzzy systems under variable sampling,” Journal of the Franklin Institute, vol. 354, no. 14, pp. 5839–5853, July 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  47. [47]
    C. Ge, H.Wang, Y. J. Liu, and J. H. Park, “Stabilization of chaotic systems under variable sampling and state quantized controller,” Fuzzy Sets and Systems, vol. 344, pp. 129–144, August 2018.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Business Technology InstituteNingbo, ZhejiangChina
  2. 2.School of Mathematics ScienceHuaiyin Normal UniversityHuaian, JiangsuChina
  3. 3.Big data instituteZhejiang Business Technology InstituteNingbo, ZhejiangChina
  4. 4.College of Information Science and TechnologyDonghua UniversityShanghaiChina

Personalised recommendations