Adaptive Synchronization of Time Delay Chaotic Systems with Uncertain and Unknown Parameters via Aperiodically Intermittent Control

  • Yuangan WangEmail author
  • Xingpeng Zhang
  • Liping Yang
  • Hong Huang


Time delay and uncertainty are the two common phenomena in nonlinear systems, which seriously influence the control and synchronization of nonlinear systems. In this paper, an adaptive intermittent control strategy is proposed to realize the synchronization of time delay chaotic systems with uncertain and unknown parameters. For the uncertain and unknown parameters, some sufficient conditions for complete synchronization are derived based on the stability theory. In the part of numerical simulation, two cases of linear and non-linear delay are discussed, which both show the effectiveness of the theoretical results.


Adaptive intermittent control synchronization time delay uncertain unknown parameters 


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  1. [1]
    R. Luo and Y. Zeng, “The control and synchronization of a class of chaotic systems with a novel input,” Chinese Journal of Physics, vol. 54, no. 1, pp. 147–158, February 2016.MathSciNetCrossRefGoogle Scholar
  2. [2]
    D. Sadaoui, A. Boukabou, and S. Hadef, “Predictive feedback control and synchronization of hyperchaotic systems,” Applied Mathematics and Computation, vol. 247, pp. 235–243, November 2014.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    S. Vaidyanathan, “Analysis and adaptive synchronization of eight-term 3-D polynomial chaotic systems with three quadratic nonlinearities,” The European Physical Journal Special Topics, vol. 223, no. 8, pp. 1519–1529, June 2014.CrossRefGoogle Scholar
  4. [4]
    H. Wang, Z. Han, Q. Xie, and W. Zhang, “Sliding mode control for chaotic systems based on LMI,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1410–1417, April 2009.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    Y. Wang, H. Yu, X. Zhang, and D. Li, “Stability analysis and design of time-varying nonlinear systems based on impulsive fuzzy model,” Discrete Dynamics in Nature & Society, vol. 2012, no. 2, pp. 373–390, 2012.Google Scholar
  6. [6]
    R. Zhang, X. Liu, D. Zeng, S. Zhong, and K. Shi, “A novel approach to stability and stabilization of fuzzy sampleddata Markovian chaotic systems,” Fuzzy Sets and Systems, vol. 344, pp. 108–128, August 2018.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    X. Zhang, A. Khadra, D. Li, and D. Yang, “Impulsive stability of chaotic systems represented by TS model,” Chaos, Solitons & Fractals, vol. 41, no. 4, pp. 1863–1869, August 2009.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    R. Zhang, D. Zeng, S. Zhong, K. Shi, and J. Cui, “New approach on designing stochastic sampled-data controller for exponential synchronization of chaotic Lur’e systems,” Nonlinear Analysis: Hybrid Systems, vol. 29, pp. 303–321, August 2018.MathSciNetzbMATHGoogle Scholar
  9. [9]
    J. Cai and M. Ma, “Synchronization between two non-autonomous chaotic systems via intermittent control of sinusoidal state error feedback,” Optik, vol. 130, pp. 455–463, February 2017.CrossRefGoogle Scholar
  10. [10]
    Y. Wang and H. Yu, “Fuzzy synchronization of chaotic systems via intermittent control,” Chaos Solitons and Fractals, vol. 106, pp. 154–160, January 2018.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    J. A. Wang and X. Y. Wen, “Pinning exponential synchronization of nonlinearly coupled neural networks with mixed delays via intermittent control,” International Journal of Control, Automation and Systems, vol. 16, no. 4, pp. 1558–1568, August 2018.CrossRefGoogle Scholar
  12. [12]
    Y. Li and C. Li, “Complete synchronization of delayed chaotic neural networks by intermittent control with two switches in a control period,” Neurocomputing, vol. 173, no. 3, pp. 1341–1347, January 2016.CrossRefGoogle Scholar
  13. [13]
    Y. Zhang and K. Li, “Successive lag synchronization on nonlinear dynamical networks via aperiodically intermittent control,” Nonlinear Dynamics, vol. 95, no. 5, pp. 3075–3089, March 2019.CrossRefGoogle Scholar
  14. [14]
    S. Cai, X. Li, P. Zhou, and J. Shen, “Aperiodic intermittent pinning control for exponential synchronization of mem-ristive neural networks with time-varying delays,” Neurocomputing, vol. 332, pp. 249–258, March 2019.CrossRefGoogle Scholar
  15. [15]
    J. Yu, C. Hu, H. Jiang, and Z. Teng, “Exponential synchronization of Cohen-Grossberg neural networks via periodically intermittent control,” Neurocomputing, vol. 74, no. 10, pp. 1776–1782, May 2011.CrossRefGoogle Scholar
  16. [16]
    J. Huang, C. Li, and X. He, “Stabilization of a memristor-based chaotic system by intermittent control and fuzzy processing,” International Journal of Control Automation and Systems, vol. 11, no. 3, pp. 643–647, June 2013.CrossRefGoogle Scholar
  17. [17]
    J. Huang, C. Li, W. Zhang, and P. Wei, “Projective synchronization of a hyperchaotic system via periodically intermittent control,” Chinese Physics B, vol. 21, no. 9, pp. 090508, 2012.Google Scholar
  18. [18]
    D. Li and X. Zhang, “Impulsive synchronization of fractional order chaotic systems with time-delay,” Neurocomputing, vol. 216, pp. 39–44, December 2016.CrossRefGoogle Scholar
  19. [19]
    W. H. Chen, Z. Jiang, J. Zhong, and X. Lu, “On designing decentralized impulsive controllers for synchronization of complex dynamical networks with nonidentical nodes and coupling delays,” Journal of the Franklin Institute, vol. 351, no. 8, pp. 4084–4110, August 2014.MathSciNetzbMATHCrossRefGoogle Scholar
  20. [20]
    A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, and I. Rei-dler, “Zero lag synchronization of chaotic systems with time delayed couplings,” Physical review letters, vol. 104, no. 11, pp. 114102, March 2010.CrossRefGoogle Scholar
  21. [21]
    O. M. Kwon, J. H. Park, and S. M. Lee, “Secure communication based on chaotic synchronization via interval time-varying delay feedback control,” Nonlinear Dynamics, vol. 63, no. 1-2, pp. 239–252, January 2011.MathSciNetzbMATHCrossRefGoogle Scholar
  22. [22]
    R. Zhang, D. Zeng, S. Zhong, and Y. Yu, “Event-triggered sampling control for stability and stabilization of memris-tive neural networks with communication delays,” Applied Mathematics and Computation, vol. 310, pp. 57–74, October 2017.MathSciNetzbMATHCrossRefGoogle Scholar
  23. [23]
    L. Pan, X. Tang, and Y. Pan, “Generalized and Exponential Synchronization for a Class of Novel Complex Dynamic Networks with Hybrid Time-varying Delay via IPAPC,” International Journal of Control, Automation and Systems, vol. 16, no. 5, pp. 2501–2517, October 2018.CrossRefGoogle Scholar
  24. [24]
    M. Zarefard and S. Effati, “Adaptive synchronization between two non-identical BAM neural networks with unknown parameters and time-varying delays,” International Journal of Control, Automation and Systems, vol. 15, no. 4, pp. 1787–887, August 2017.CrossRefGoogle Scholar
  25. [25]
    R. Zhang, D. Zeng, J. H. Park, Y. Liu, and S. Zhong, “Quantized sampled-data control for synchronization of in-ertial neural networks with heterogeneous time-varying delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 12, pp. 6385–6395, December 2018.MathSciNetCrossRefGoogle Scholar
  26. [26]
    Y. Wang, J. Hao, and Z. Zuo, “A new method for exponential synchronization of chaotic delayed systems via intermittent control,” Physics Letters A, vol. 374, no. 19, pp. 2024–2029, April 2010.MathSciNetzbMATHCrossRefGoogle Scholar
  27. [27]
    G. Zhang and Y. Shen, “Exponential synchronization of delayed memristor-based chaotic neural networks via periodically intermittent control,” Neural Networks, vol. 55, pp. 1–10, July 2014.zbMATHCrossRefGoogle Scholar
  28. [28]
    S. Cai, P. Zhou, and Z. Liu, “Intermittent pinning control for cluster synchronization of delayed heterogeneous dynamical networks,” Nonlinear Analysis: Hybrid Systems, vol. 18, pp. 134–155, November 2015.MathSciNetzbMATHGoogle Scholar
  29. [29]
    M. Liu, H. Jiang, and C. Hu, “Synchronization of hybridcoupled delayed dynamical networks via aperiodically intermittent pinning control,” Journal of the Franklin Institute, vol. 353, no. 12, pp. 2722–2742, August 2016.MathSciNetzbMATHCrossRefGoogle Scholar
  30. [30]
    D. Li, X. Zhang, Y. Hu, and Y. Yang, “Adaptive impulsive synchronization of fractional order chaotic system with uncertain and unknown parameters,” Neurocomputing, vol. 167, pp. 165–171, November 2015.CrossRefGoogle Scholar
  31. [31]
    X. Chen, J. H. Park, J. Cao, and J. Qiu, “Adaptive synchronization of multiple uncertain coupled chaotic systems via sliding mode control,” Neurocomputing, vol. 273, pp. 9–21, January 2018.CrossRefGoogle Scholar
  32. [32]
    X. Li, Y. D. Chu, A. Y. T. Leung, and H. Zhang, “Synchronization of uncertain chaotic systems via complete-adaptive-impulsive controls,” Chaos, Solitons & Fractals, vol. 100, pp. 24–30, July 2017.MathSciNetzbMATHCrossRefGoogle Scholar
  33. [33]
    S. Mobayen, “Design of LMIbased global sliding mode controller for uncertain nonlinear systems with application to Genesio’s chaotic system,” Complexity, vol. 21, no. 1, pp. 94–98, October 2015.MathSciNetCrossRefGoogle Scholar
  34. [34]
    M. P. Aghababa, S. Khanmohammadi, and G. Alizadeh, “Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique,” Applied Mathematical Modelling, vol. 35, no. 6, pp. 3080–3091, June 2011.MathSciNetzbMATHCrossRefGoogle Scholar
  35. [35]
    J. Sun, Y. Wu, Y. Wang, and Y. Shen, “Finite-time synchronization between two complex-variable chaotic systems with unknown parameters via nonsingular terminal sliding mode control,” Nonlinear Dynamics, vol. 85, no. 2, pp. 1105–1117, July 2016.MathSciNetzbMATHCrossRefGoogle Scholar
  36. [36]
    X. Gao, M. Cheng, and H. Hu, “Adaptive impulsive synchronization of uncertain delayed chaotic system with full unknown parameters via discretetime drive signals,” Complexity, vol. 21, no. 5, pp. 43–51, June 2016.MathSciNetCrossRefGoogle Scholar
  37. [37]
    Y. Ji, X. Liu, and F. Ding, “New criteria for the robust impulsive synchronization of uncertain chaotic delayed nonlinear systems,” Nonlinear Dynamics, vol. 79, no. 1, pp. 1–9, January 2015.MathSciNetzbMATHCrossRefGoogle Scholar
  38. [38]
    X. Yang, Q. Zhu, and C. Huang, “Lag stochastic synchronization of chaotic mixed time-delayed neural networks with uncertain parameters or perturbations,” Neurocomputing, vol. 74, no. 10, pp. 1617–1625, May 2011.CrossRefGoogle Scholar
  39. [39]
    C. Zheng and J. Cao, “Robust synchronization of coupled neural networks with mixed delays and uncertain parameters by intermittent pinning control,” Neurocomputing, vol. 141, pp. 153–159, October 2014.CrossRefGoogle Scholar
  40. [40]
    W. Zhang, C. Li, T. Huang, and T. J. Huang, “Stability and synchronization of memristor-based coupling neural networks with time-varying delays via intermittent control,” Neurocomputing, vol. 173, pp. 1066–1072, January 2016.CrossRefGoogle Scholar
  41. [41]
    Z. Wang, X. Huang, and G. Shi, “Analysis of nonlinear dynamics and chaos in a fractional order financial system with time delay,” Computers and Mathematics With Applications, vol. 62, no. 3, pp. 1531–1539, August 2011.MathSciNetzbMATHCrossRefGoogle Scholar
  42. [42]
    X. Zhang, X. Zhang, D. Li, and D. Yang, “Adaptive synchronization for a class of fractional order time-delay uncertain chaotic systems via fuzzy fractional order neural network,” International Journal of Control, Automation, and Systems, vol. 17, no. 5, pp. 1209–1220, May 2019.CrossRefGoogle Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  • Yuangan Wang
    • 1
    Email author
  • Xingpeng Zhang
    • 2
  • Liping Yang
    • 3
  • Hong Huang
    • 3
  1. 1.The School of ScienceBeibu Gulf UniversityGuangxiChina
  2. 2.School of Big Data and Software EngineeringChongqing UniversityChongqingChina
  3. 3.The Key Laboratory of Optoelectronic Technology and Systems of Education Ministry of ChinaChongqing UniversityChongqingChina

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