Skip to main content
SpringerLink
Log in

Robust synchronization of uncertain chaotic neural networks with randomly occurring uncertainties and non-fragile output coupling delayed feedback controllers

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper deals with the synchronization control problem for the uncertain chaotic neural networks with randomly occurring uncertainties and randomly occurring control gain fluctuations. By introducing an improved Lyapunov–Krasovskii functional and employing reciprocally convex approach, a delay-dependent non-fragile output feedback controller is designed to achieve synchronization with the help of a drive–response system and the linear matrix inequality approach. Finally, numerical results and its simulations are given to show the effectiveness of the derived results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chen, G., Dong, X.: From Chaos to Order. World Scientific, (1997)

  3. Kwon, O.M., Park, J.H., Lee, S.M.: Secure communication based on chaotic synchronization via interval time-varying delay feedback control. Nonlinear Dyn. 63, 239–252 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Akhavan, A., Samsudin, A., Akhshani, A.: A symmetric image encryption scheme based on combination of nonlinear chaotic maps. J. Franklin Inst. 348, 1797–1813 (2011)

    Article  MathSciNet  Google Scholar 

  5. Li, C., Li, Y.: Fast and robust image segmentation by small-world neural oscillator networks. Cogn. Neurodyn. 5, 209–220 (2011)

    Article  Google Scholar 

  6. Yoshida, H., Kurata, S., Li, Y., Nara, S.: Chaotic neural network applied to two-dimensional motion control. Cogn. Neurodyn. 4, 69–80 (2010)

    Article  Google Scholar 

  7. Cheng, C.-J., Liao, T.-L., Hwang, C.-C.: Exponential synchronization of a class of chaotic neural networks. Chaos Solitons Fractals 24, 197–206 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gao, X., Zhong, S., Gao, F.: Exponential synchronization of neural networks with time-varying delays. Nonlinear Anal. 71, 2003–2011 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Li, C., Chen, L., Aihara, K.: Impulsive control of stochastic systems with applications in chaos control, chaos synchronization, and neural networks. Chaos 18, 023132 (2008)

    Article  MathSciNet  Google Scholar 

  10. Yang, X., Huang, C., Zhu, Q.: Synchronization of switched neural networks with mixed delays via impulsive control. Chaos Solitons Fractals 44, 817–826 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Li, X., Rakkiyappan, R.: Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays. Commun. Nonlinear Sci. Numer. Simulat. 18, 1515–1523 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wu, Z., Fu, X.: Combination synchronization of three different order nonlinear systems using active backstepping design. Nonlinear Dyn. 73, 1863–1872 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lü, L., Li, Y., Fan, X., Lü, N.: Outer synchronization between uncertain complex networks based on backstepping design. Nonlinear Dyn. 73, 767–773 (2013)

    Article  MATH  Google Scholar 

  14. Chen, C.-K., Yan, J.-J., Liao, T.-L.: Sliding mode control for synchronization of Rössler systems with time delays and its application to secure communication. Phys. Scr. 76, 436–441 (2007)

    Article  MATH  Google Scholar 

  15. Martinez-Guerra, R., Yu, W.: Chaotic synchronization and secure communication via sliding-mode observer. Int. J. Bifurcation Chaos 18, 235–243 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.: Synchronization in complex networks. Phys. Rep. 469, 93–153 (2008)

    Article  MathSciNet  Google Scholar 

  17. Sun, Y., Cao, J., Wang, Z.: Exponential synchronization of stochastic perturbed chaotic delayed neural networks. Neurocomputing 70, 2477–2485 (2007)

    Article  Google Scholar 

  18. Park, J.H.: Synchronization of cellular neural networks of neutral type via dynamic feedback controller. Chaos Solitons Fractals 42, 1299–1304 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  19. Shi, Y., Zhu, P.: Adaptive synchronization of different Cohen-Grossberg chaotic neural networks with unknown parameters and time-varying delays. Nonlinear Dyn. 73, 1721–1728 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  20. Yu, W., Cao, J.: Cryptography based on delayed chaotic neural networks. Phys. Lett. A 356, 333–338 (2006)

    Article  MATH  Google Scholar 

  21. Yang, J., Liao, X., Yu, W., Wong, K., Wei, J.: Cryptanalysis of a cryptographic scheme based on delayed chaotic neural networks. Chaos Solitons Fractals 40, 821–825 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. Vembarasan, V., Balasubramaniam, P.: Chaotic synchronization of Rikitake system based on T-S fuzzy control techniques. Nonlinear Dyn. 74, 31–44 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  23. Tang, Y., Fang, J.-A., Miao, Q.-Y.: Synchronization of stochastic delayed neural networks with Markovian switching and its application. Int. J. Neural Syst. 19, 43–56 (2009)

    Article  Google Scholar 

  24. Balasubramaniam, P., Vembarasan, V., Rakkiyappan, R.: Delay-dependent robust exponential state estimation of Markovian jumping fuzzy Hopfield neural networks with mixed random time-varying delays. Commun. Nonlinear Sci. Numer. Simulat. 16, 2109–2129 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  25. Kan, X., Wang, Z., Shu, H.: State estimation for discrete-time delayed neural networks with fractional uncertainties and sensor saturations. Neurocomputing. 117, 64–71 (2013)

    Article  Google Scholar 

  26. Ma, L., Wang, Z., Bo, Y., Guo, Z.: A game theory approach to mixed \(H_{2}/H_{\infty }\) control for a class of stochastic time-varying systems with randomly occurring nonlinearities. Systems Control Lett. 60, 1009–1015 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  27. Hu, J., Wang, Z., Gao, H., Stergioulas, L.K.: Robust sliding mode control for discrete stochastic systems with mixed time delays, randomly occurring uncertainties, and randomly occurring nonlinearities. IEEE Trans. Industrial Electronics 59, 3008–3015 (2012)

    Article  Google Scholar 

  28. Wu, Z.-G., Park, J.H., Su, H., Chu, J.: Robust dissipativity analysis of neural networks with time-varying delay and randomly occurring uncertainties. Nonlinear Dyn. 69, 1323–1332 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  29. Lee, T.H., Park, J.H., Wu, Z.-G., Lee, S.-C., Lee, D.H.: Robust \(H_\infty \) decentralized dynamic control for synchronization of a complex dynamical network with randomly occurring uncertainties. Nonlinear Dyn. 70, 559–570 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  30. Dong, H., Wang, Z., Chen, X., Gao, H.: A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information. Math. Prob. Engg. 2012, 1–15 (2012)

    MathSciNet  Google Scholar 

  31. Lee, T.H., Park, J.H., Kwon, O.M., Lee, S.M.: Robust synchronisation of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control. Int. J. Control 86, 107–119 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  32. Lakshmanan, S., Park, J.H., Jung, H.Y., Balasubramaniam, P., Lee, S.M.: Design of state estimator for genetic regulatory networks with time-varying delays and randomly occurring uncertainties. BioSystems 111, 51–70 (2013)

    Article  Google Scholar 

  33. Li, T., Fei, S.-M., Zhang, K.-J.: Synchronization control of recurrent neural networks with distributed delays. Phys. A 387, 982–996 (2008)

    Article  Google Scholar 

  34. Li, T., Fei, S.-M., Zhu, Q., Cong, S.: Exponential synchronization of chaotic neural networks with mixed delays. Neurocomputing 71, 3005–3019 (2008)

    Article  Google Scholar 

  35. Park, J.H., Kwon, O.M.: Guaranteed cost control of time-delay chaotic systems. Chaos Solitons Fractals 27, 1011–1018 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  36. Yu, W., Cao, J.: Synchronization control of stochastic delayed neural networks. Phys. A 373, 252–260 (2007)

    Article  Google Scholar 

  37. Li, X., Bohner, M.: Exponential synchronization of chaotic neural networks with mixed delays and impulsive effects via output coupling with delay feedback. Math. Comput. Modelling 52, 643–653 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  38. Li, X., Ding, C., Zhu, Q.: Synchronization of stochastic perturbed chaotic neural networks with mixed delays. J. Franklin Inst. 347, 1266–1280 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  39. Balasubramaniam, P., Vembarasan, V.: Synchronization of recurrent neural networks with mixed time-delays via output coupling with delayed feedback. Nonlinear Dyn. 70, 677–691 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  40. Lien, C.-H., Cheng, W.-C., Tsai, C.-H., Yu, K.-W.: Non-fragile observer-based controls of linear system via LMI approach. Chaos Solitons Fractals 32, 1530–1537 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  41. Liu, L., Han, Z., Li, W.: Non-fragile observer-based passive control for uncertain time delay systems subjected to input nonlinearity. Nonlinear Anal. 73, 2603–2610 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  42. Wu, Z.-G., Park, J.H., Su, H., Chu, J.: Non-fragile synchronisation control for complex networks with missing data. Int. J. Control 86, 555–566 (2012)

    Article  MathSciNet  Google Scholar 

  43. Tang, Y., Wong, W.K.: Distributed synchronization of coupled neural networks via randomly occurring control. IEEE Trans. Neural Netw. Learning Syst. 24, 435–447 (2013)

  44. Fang, M., Park, J.H.: Non-fragile synchronization of neural networks with time-varying delay and randomly occurring controller gain fluctuation. Appl. Math. Comput. 219, 8009–8017 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  45. Boyd S., Ghaoui L.El., Feron E., Balakrishnan V.: Linear Matrix Inequalities in Systems and Control Theory. SIAM, Philadelphia (1994).

  46. Gu, K., Kharitonov, V.L., Chen, J.: Stability of Time-Delay Systems. Birkhäuser, Boston (2003)

    Book  MATH  Google Scholar 

  47. Park, P.G., Ko, J.W., Jeong, C.: Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47, 235–238 (2011)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to express their sincere gratitude to the Editor-in-Chief, Associate Editor, and Anonymous Reviewers for their valuable comments and suggestions to improve the quality of the manuscript. The research work of Mr. V. Vembarasan is supported by DST INSPIRE Fellowship Grant DST/INSPIRE Fellowship/2011/278 dated 21.12.2011 and 03.10.2012, from Ministry of Science and Technology, Government of India; Also this research work is supported by the High Impact Research MoE Grant UM.C/625/1/HIR/ MoHE/FCSIT/08, H-22001-00-B0008 from the Ministry of Higher Education Malaysia.

Author information

Authors and Affiliations

  1. Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram , 624 302, Tamilnadu, India

    V. Vembarasan & P. Balasubramaniam

  2. Faculty of Computer Science and Information Technology, Centre of Image and Signal Processing, University of Malaya, Kuala Lumpur , 50603, Malaysia

    V. Vembarasan & Chee Seng Chan

Authors
  1. V. Vembarasan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Balasubramaniam
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chee Seng Chan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Balasubramaniam.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vembarasan, V., Balasubramaniam, P. & Chan, C.S. Robust synchronization of uncertain chaotic neural networks with randomly occurring uncertainties and non-fragile output coupling delayed feedback controllers. Nonlinear Dyn 78, 2031–2047 (2014). https://doi.org/10.1007/s11071-014-1586-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1586-8

Keywords

Search

Navigation