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Adaptive synchronization of T-S fuzzy complex networks with time-varying delays via the pinning control method

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Abstract

In this paper, the synchronization of Takagi–Sugeno (T-S) fuzzy complex networks with time-varying delays and adaptive coupling weights is studied. Using the pinning control and adaptive feedback strategy, a new general class of complex networks with fuzzy logic is proposed and its synchronization is investigated in terms of linear matrix inequalities (LMIs). The adaptive update law of coupling weight is only related to the dynamical behaviors of directly connected nodes. Based on the Lyapunov stability theory, it is proven that the synchronization of the addressed network can be achieved under those control strategies. Finally, two numerical examples are given to verify the effectiveness of our theoretical results.

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References

  1. Lu, J., Cao, J.: Adaptive synchronization of uncertain dynamical networks with delayed coupling. Nonlinear Dyn. 53(1–2), 107–115 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Rao, P., Wu, Z., Liu, M.: Adaptive projective synchronization of dynamical networks with distributed time delays. Nonlinear Dyn. 67(3), 1729–1736 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhang, Q.J., Zhao, J.C.: Projective and lag synchronization between general complex networks via impulsive control. Nonlinear Dyn. 67, 2519–2525 (2012)

    Article  MATH  Google Scholar 

  4. Liu, T., Zhao, J., Hill, D.J.: Synchronization of complex delayed dynamical networks with nonlinearly coupled nodes. Chaos Solitons Fractals 40, 1506–1519 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Lee, T.H., Wu, Z.G., Park, J.H.: Synchronization of a complex dynamical network with coupling time-varying delays via sampled-data control. Appl. Math. Comput. 219, 1354–1366 (2012)

    Article  MathSciNet  Google Scholar 

  6. Ji, D.H., Jeong, S.C., Park, J.H., Lee, S.M., Won, S.C.: Adaptive lag synchronization for uncertain complex dynamical network with delayed coupling. Appl. Math. Comput. 218, 4872–4880 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lu, J.Q., Kurths, J., Cao, J.D., Mahdavi, N., Huang, C.: Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy. IEEE Trans. Neural Netw. Learning Syst. 23(2), 285–292 (2012)

    Article  Google Scholar 

  8. Zheng, S.: Adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling. Nonlinear Dyn. 67, 2621–2630 (2012)

    Article  MATH  Google Scholar 

  9. Wang, Z., Wang, Y., Liu, Y.: Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays. IEEE Trans. Neural Netw. 21, 11–25 (2010)

    Article  Google Scholar 

  10. Fei, Z.Y., Gao, H.J., Zheng, W.X.: New synchronization stability of complex networks with an interval time-varying coupling delay. IEEE Trans. Circuits Syst. II, Express Briefs 56, 499–503 (2009)

    Article  Google Scholar 

  11. Carroll, T.L., Pecora, L.M.: Synchronization in chaotic circuits. IEEE Trans. Circuits Syst. 38, 453–456 (1991)

    Article  Google Scholar 

  12. Feki, M.: Sliding mode control and synchronization of chaotic systems with parametric uncertainties. Chaos Solitons Fractals 41(3), 1390–1400 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Wedekind, I., Parlitz, U.: Experimental observation of synchronization and anti-synchronization of chaotic lowfrequency-fluctuations in external cavity semiconductor lasers. Int. J. Bifurc. Chaos Appl. Sci. Eng. 11, 1141–1147 (2001)

    Article  Google Scholar 

  14. Wang, Y.W., Wen, C.Y., Yang, M., Xiao, J.W.: Adaptive control and synchronization for chaotic systems with parametric uncertainties. Phys. Lett. A 372(14), 2409–2414 (2008)

    Article  MATH  Google Scholar 

  15. Cao, J., Chen, G., Li, P.: Global synchronization in an array of delayed neural networks with hybrid coupling. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 38, 488–498 (2008)

    Article  Google Scholar 

  16. Chen, M., Chen, W.H.: Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems. Chaos Solitons Fractals 41(5), 2716–2724 (2009)

    Article  MATH  Google Scholar 

  17. Ren, F.L., Cao, J.D.: Anti-synchronization of stochastic perturbed delayed chaotic neural networks. Neural Comput. Appl. 18, 515–521 (2009)

    Article  Google Scholar 

  18. Wang, Z., Wang, Y., Liu, Y.: Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays. IEEE Trans. Neural Netw. 21, 11–25 (2010)

    Article  Google Scholar 

  19. Wang, B., Guan, Z.: Chaos synchronization in general complex dynamical networks with coupling delays. Nonlinear Anal., Real World Appl. 11, 1925–1932 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  20. Cao, J., Li, L.: Cluster synchronization in an array of hybrid coupled neural networks with delay. Neural Netw. 22, 335–342 (2009)

    Article  Google Scholar 

  21. Hu, C., Yu, J., Jiang, H.J., Teng, Z.D.: Pinning synchronization of weighted complex networks with variable delays and adaptive coupling weights. Nonlinear Dyn. 67, 1373–1385 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  22. Yu, W., Chen, G., Lü, J.: On pinning synchronization of complex dynamical networks. Automatica 45, 429–435 (2009)

    Article  MATH  Google Scholar 

  23. Song, Q., Cao, J.: On pinning synchronization of directed and undirected complex dynamical networks. IEEE Trans. Circuits Syst. I, Regul. Pap. 57, 672–680 (2010)

    Article  MathSciNet  Google Scholar 

  24. Xiang, L., Zhu, J.: On pinning synchronization of general coupled networks. Nonlinear Dyn. 64(4), 339–348 (2011)

    Article  MathSciNet  Google Scholar 

  25. Zhao, J., Lu, J., Zhang, Q.: Pinning a complex delayed dynamical network to a homogenous trajectory. IEEE Trans. Circuits Syst. II, Express Briefs 56, 514–518 (2009)

    Article  Google Scholar 

  26. Li, X., Wang, X., Chen, G.: Pinning a complex dynamical network to its equilibrium. IEEE Trans. Circuits Syst. I, Regul. Pap. 51, 2074–2087 (2004)

    Article  MathSciNet  Google Scholar 

  27. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985)

    Article  MATH  Google Scholar 

  28. Tang, Y., Fang, J.A., Xia, M., Gu, X.J.: Synchronization of Takagi–Sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays. Appl. Math. Model. 34, 843–855 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  29. Tang, Y., Fang, J., Xia, M.: Synchronization of Takagi–Sugeno fuzzy stochastic complex networks with mixed delays. Intell. Comput. Technol. Autom. 2, 810–813 (2009)

    Google Scholar 

  30. Gong, D.W., Zhang, H.G., Wang, Z.S., Liu, J.H.: Synchronization analysis for complex networks with coupling delay based on T-S fuzzy theory. Appl. Math. Model. 36, 6215–6224 (2012)

    Article  MathSciNet  Google Scholar 

  31. Park, M.J., Kwon, O.M., Park, J.H., Lee, S.M., Cha, E.J.: Synchronization criteria of fuzzy complex dynamical networks with interval time-varying delays. Appl. Math. Comput. 218, 11634–11647 (2012)

    Article  MathSciNet  Google Scholar 

  32. Li, C., Chen, G.: Synchronization in general complex dynamical networks with coupling delays. Physica A 343, 263–278 (2004)

    Article  MathSciNet  Google Scholar 

  33. Liu, T., Dimirovski, G.M., Zhao, J.: Exponential synchronization of complex delayed dynamical networks with general topology. Physica A 387, 643–652 (2008)

    Article  Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (60835004, 60964001, 61263013). The Science Foundation Project of Guangxi Province (0991019Z), Guangxi Experiment Center of Information Science (20130110), and Major Research Project of Guangxi Department of Education (201101ZD007).

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Authors and Affiliations

  1. College of Electronic Engineering and Automation, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, P.R. China

    Xiru Wu & Xuanju Dang

  2. College of Electric and Information Technology, Hunan University, Changsha, Hunan, 410082, P.R. China

    Yaonan Wang

  3. Hunan Women’s University, Changsha, Hunan, 410004, P.R. China

    Lihong Huang

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  1. Xiru Wu
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  2. Yaonan Wang
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  3. Xuanju Dang
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  4. Lihong Huang
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Correspondence to Xiru Wu.

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Wu, X., Wang, Y., Dang, X. et al. Adaptive synchronization of T-S fuzzy complex networks with time-varying delays via the pinning control method. Nonlinear Dyn 74, 143–152 (2013). https://doi.org/10.1007/s11071-013-0954-0

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  • DOI: https://doi.org/10.1007/s11071-013-0954-0

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