Skip to main content
SpringerLink
Log in

Delay-range-dependent local adaptive and robust adaptive synchronization approaches for time-delay chaotic systems

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

Abstract

This paper studies the local adaptive and robust adaptive control methodologies for the synchronization of the chaotic drive and the response systems with finite time lags, bounded delay rates, unknown parameters, and perturbations. A local adaptive coherence control condition under bounded initial condition is developed to synthesize a feedback controller capable of executing successful synchronization of the drive and the response systems with uncertain parameters and delay belonging to a range (with either zero or nonzero lower bound). A sufficiency condition for the adaptive control approach is inculcated through an amendment in the conventional Lyapunov–Krasovskii functional, which enables to develop the adaptation laws for the unknown parameters associated with the nonlinearity in the dynamical behavior of the drive and the response systems. Further, a robust adaptive synchronization control condition for asymptotic convergent behavior of the synchronization error to a bounded region under perturbations as well as disturbances is provided. Indifferent to the existing works, delay-range-dependent adaptive synchronization methodologies are derived in this paper, and the rendered controller design conditions are valid for both the slow and the fast variations in time delays. Numerical simulations for the chaotic delayed Hopfield neural networks are presented to elaborate the efficacy of the proposed delay-range-dependent adaptive and robust adaptive synchronization control methodologies.

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

Similar content being viewed by others

References

  1. Yang, J., Chen, Y., Zhu, F.: Associated observer-based synchronization for uncertain chaotic systems subject to channel noise and chaos-based secure communication. Neurocomputing 167, 587–595 (2015)

    Article  Google Scholar 

  2. Yu, W.T., Tang, J., Ma, J., Luo, J.M., Yang, X.Q.: Damped oscillations in a multiple delayed feedback NF-B signaling module. Eur. Biophys. J. 44(8), 677–684 (2015)

    Article  Google Scholar 

  3. Siddique, M., Rehan, M.: A concept of coupled chaotic synchronous observers for nonlinear and adaptive observers-based chaos synchronization. Nonlinear Dyn. 84, 2251–2272 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  4. Shahverdiev, E.M., Shore, K.A.: Synchronization of chaos in unidirectionally and bidirectionally coupled multiple time delay laser diodes with electro-optical feedback. Opt. Commun. 282(2), 310–316 (2009)

    Article  Google Scholar 

  5. Wickramasinghe, M., Kiss, I.Z.: Spatially organized dynamical states in chemical oscillator networks: synchronization dynamical differentiation and chimera patterns. PloS ONE 8(11), e80586 (2013)

    Article  Google Scholar 

  6. Yang, X., Cao, J., Yang, Z.: Synchronization of coupled reaction–diffusion neural networks with time-varying delays via pinning-impulsive controller. SIAM J. Control Optim. 51(5), 3486–3510 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. Rau, A.W., Nill, S., Eidens, R.S., Oelfke, U.: Synchronized tumor tracking with electromagnetic transponders and kV X-ray imaging: evaluation based on a thorax phantom. Phys. Med. Biol. 53(14), 3789–3805 (2008)

    Article  Google Scholar 

  8. Wenxiu, Z., Jun, L., Lili, P., Jian, C.: Application of RS485 for communication and synchronization in distributed electromagnetic exploration system. In: Proceedings of Electric Information and Control Engineering (ICEICE), Wuhan, pp. 4815–4818 (2011)

  9. Wei, G.W., Jia, Y.Q.: Synchronization-based image edge detection. Europhys. Lett. 59(6), 814–819 (2002)

    Article  Google Scholar 

  10. Elfring, G.J., Pak, O.S., Lauga, E.: Two-dimensional flagellar synchronization in viscoelastic fluids. J. Fluid Mech. 646, 505–515 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Sato, D., Xie, L.H., Sovari, A.A., Tran, D.X., Morita, N., Xie, F., Karagueuzian, H., Garfinkel, A., Weiss, J.N., Qu, Z.: Synchronization of chaotic early after depolarizations in the genesis of cardiac arrhythmias. Proc. Natl. Acad. Sci. USA 106(9), 2983–2988 (2009)

    Article  Google Scholar 

  12. Yao, C.G., Ma, J., Li, C., He, Z.W.: The effect of process delay on dynamical behaviors in a self-feedback nonlinear oscillator. Commun. Nonlinear Sci. Numer. Simul. 39, 99–107 (2016)

    Article  MathSciNet  Google Scholar 

  13. Tian, J.K., Liu, Y.M.: Improved delay-dependent stability analysis for neural networks with interval time-varying delays. Math. Probl. Eng. Article ID 705367 (2015)

  14. Rong, R.Z., Tian, J.K.: Improved stability analysis for neural networks with interval time-varying delays. Appl. Mech. Mater. 687, 2078–2082 (2014)

    Google Scholar 

  15. Guan, Z.H., Liu, Z.W., Feng, G., Wang, Y.W.: Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control. IEEE Trans. Circuits Syst. I Regul. Pap. 57(8), 2182–2195 (2010)

  16. Zhu, Q., Cao, J.: Adaptive synchronization of chaotic Cohen–Crossberg neural networks with mixed time delays. Nonlinear Dyn. 61(3), 517–534 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Lin, T.C., Lee, T.Y.: Chaos synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive fuzzy sliding mode control. IEEE Trans. Fuzzy Syst. 19(4), 623–635 (2011)

    Article  Google Scholar 

  18. 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. Ind. Electron. 59(7), 3008–3015 (2012)

    Article  Google Scholar 

  19. Li, Z., Cao, X., Ding, N.: Adaptive fuzzy control for synchronization of nonlinear teleoperators with stochastic time-varying communication delays. IEEE Trans. Fuzzy Syst. 19(4), 745–757 (2011)

    Article  Google Scholar 

  20. Rafique, M.A., Rehan, M., Siddique, M.: Adaptive mechanism for synchronization of chaotic oscillators with interval time-delays. Nonlinear Dyn. 81(1), 495–509 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  21. He, P., Jing, C.G., Fan, T., Chen, C.Z.: Robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties. Complexity 19(3), 10–26 (2014)

    Article  MathSciNet  Google Scholar 

  22. Wang, T., Zhou, W., Zhao, S., Yu, W.Q.: Robust master–slave synchronization for general uncertain delayed dynamical model based on adaptive control scheme. ISA Trans. 53(2), 335–340 (2014)

    Article  Google Scholar 

  23. Yang, X.S., Cao, J., Long, Y., Rui, W.: Adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations. IEEE Trans. Neural Netw. Learn. Syst. 21(10), 1656–1667 (2010)

    Article  Google Scholar 

  24. Lu, J., Cao, J., Ho, D.W.: Adaptive stabilization and synchronization for chaotic Lur’e systems with time-varying delay. IEEE Trans. Circuits Syst. I Regul. Pap. 55(5), 1347–1356 (2008)

  25. Farid, Y., Bigdeli, N.: Robust adaptive intelligent sliding model control for a class of uncertain chaotic systems with unknown time-delay. Nonlinear Dyn. 67(3), 2225–2240 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  26. Yue, D., Li, H.: Synchronization stability of continuous/discrete complex dynamical networks with interval time-varying delays. Neurocomputing 73(4–6), 809–819 (2010)

    Article  Google Scholar 

  27. Zhang, H., Gong, D., Chen, B., Liu, Z.: Synchronization for coupled neural networks with interval delay: a novel augmented Lyapunov–Krasovskii functional method. IEEE Trans. Neural Netw. Learn. Syst. 24(1), 58–70 (2013)

    Article  Google Scholar 

  28. Karimi, H.R., Maass, P.: Delay-range-dependent exponential \(H_\infty \) synchronization of a class of delayed neural networks. Chaos Solitons Fractals 41(3), 1125–1135 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. Shao, H.: Improved delay-dependent stability criteria for systems with a delay varying in a range. Automatica 44(12), 3215–3218 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  30. Ahmad, S., Majeed, R., Hong, K.S., Rehan. M.: Observer design for one-sided Lipschitz nonlinear systems subject to measurement delays. Math. Probl. Eng. Article ID 879492 (2015)

  31. Majeed, R., Ahmad, S., Rehan, M.: Delay-range-dependent observer-based control of nonlinear systems under input and output time-delays. Appl. Math. Comput. 262, 145–159 (2015)

    MathSciNet  Google Scholar 

  32. Lee, S.H., Park, M.J., Kwon, O.M., Sakthivel, R.: Master–slave synchronization for nonlinear systems via reliable control with gaussian stochastic process. Appl. Math. Comput. 290, 439–459 (2016)

    MathSciNet  Google Scholar 

  33. Kaviarasan, B., Sakthivel, R., Lim, Y.: Synchronization of complex dynamical networks with uncertain inner coupling and successive delays based on passivity theory. Neurocomputing 186, 127–138 (2016)

    Article  Google Scholar 

  34. Mathiyalagan, K., Anbuvithya, R., Sakthivel, R., Park, J.H., Prakash, P.: Non-fragile \(H_{\infty }\) synchronization of memristor-based neural networks using passivity theory. Neural Netw. 74, 85–100 (2016)

    Article  Google Scholar 

  35. Ma, J., Qin, H.X., Song, X.L., Chu, R.T.: Pattern selection in neuronal network driven by electric autapses with diversity in time delays. Int. J. Mod. Phys. B. 29(01). Article ID 1450239 (2015)

  36. Ahn, C.K.: Adaptive \(H_\infty \) anti-synchronization for time-delayed chaotic neural networks. Prog. Theor. Phys. 122(6), 1391–1403 (2009)

    Article  MATH  Google Scholar 

  37. Hussain, M., Rehan, M.: Nonlinear time-delay anti-windup compensator synthesis for nonlinear time-delay systems: a delay-range-dependent approach. Neurocomputing 186, 54–65 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by Higher Education Commission (HEC) of Pakistan by supporting PhD studies of the first author through indigenous PhD scholarship program (phase II, batch II, 2013).

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Pakistan Institute of Engineering and Applied Sciences (PIEAS), P.O. Box 45650, Islamabad, Pakistan

    Muhammad Siddique, Muhammad Rehan & Shakeel Ahmed

  2. Department of Electrical Engineering, NFC Institute of Engineering and Technology, Multan, Pakistan

    M. K. L. Bhatti

Authors
  1. Muhammad Siddique
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Muhammad Rehan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. K. L. Bhatti
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shakeel Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Rehan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Siddique, M., Rehan, M., Bhatti, M.K.L. et al. Delay-range-dependent local adaptive and robust adaptive synchronization approaches for time-delay chaotic systems. Nonlinear Dyn 88, 2671–2691 (2017). https://doi.org/10.1007/s11071-017-3402-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-017-3402-8

Keywords

Search

Navigation