Skip to main content
SpringerLink
Log in

Neural network-based synchronization of uncertain chaotic systems with unknown states

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In this paper, synchronization of chaotic systems with unknown parameters and unmeasured states is investigated. Two nonidentical chaotic systems in the framework of a master and a slave are considered for synchronization. It is assumed that both systems have uncertain dynamics, and states of the slave system are not measured. To tackle this challenging synchronization problem, a novel neural network-based adaptive observer and an adaptive controller have been designed. Moreover, a neural network is utilized to approximate the unknown dynamics of the slave system. The proposed method imposes neither restrictive assumption nor constraint on the dynamics of the systems. Furthermore, the stability of the entire closed-loop system in the presence of the observer dynamics has been established. Finally, effectiveness of the proposed scheme is demonstrated via computer simulation.

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

Similar content being viewed by others

References

  1. Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821

    Article  MathSciNet  MATH  Google Scholar 

  2. El-Dessoky M, Yassen M (2012) Adaptive feedback control for chaos control and synchronization for new chaotic dynamical system. Math Probl Eng. doi:10.1155/2012/347210

    MathSciNet  MATH  Google Scholar 

  3. Sudheer KS, Sabir M (2011) Adaptive modified function projective synchronization of multiple time-delayed chaotic Rossler system. Phys Lett A 375(8):1176–1178

    Article  MATH  Google Scholar 

  4. Yang J, Zhu F (2013) Synchronization for chaotic systems and chaos-based secure communications via both reduced-order and step-by-step sliding mode observers. Commun Nonlinear Sci Numer Simul 18(4):926–937

    Article  MathSciNet  MATH  Google Scholar 

  5. Abualnaja KM, Mahmoud EE (2014) Analytical and numerical study of the projective synchronization of the chaotic complex nonlinear systems with uncertain parameters and its applications in secure communication. Math Probl Eng. doi:10.1155/2014/808375

    MathSciNet  Google Scholar 

  6. Zhu F (2009) Observer-based synchronization of uncertain chaotic system and its application to secure communications. Chaos Solitons Fractals 40(5):2384–2391

    Article  MATH  Google Scholar 

  7. Aghababa MP, Heydari A (2012) Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities. Appl Math Model 36(4):1639–1652

    Article  MathSciNet  MATH  Google Scholar 

  8. Shi Y, Zhu P, Qin K (2014) Projective synchronization of different chaotic neural networks with mixed time delays based on an integral sliding mode controller. Neurocomputing 123:443–449

    Article  Google Scholar 

  9. Feng G, Cao J (2013) Master–slave synchronization of chaotic systems with a modified impulsive controller. Adv Differ Equ 1:1–12

    MathSciNet  Google Scholar 

  10. Cao J, Ho DW, Yang Y (2009) Projective synchronization of a class of delayed chaotic systems via impulsive control. Phys Lett A 373(35):3128–3133

    Article  MathSciNet  MATH  Google Scholar 

  11. He W, Cao J (2009) Generalized synchronization of chaotic systems: an auxiliary system approach via matrix measure. Chaos: an Interdisciplinary. J Nonlinear Sci 19(1):013118

    MathSciNet  MATH  Google Scholar 

  12. Bhalekar S, Daftardar-Gejji V (2010) Synchronization of different fractional order chaotic systems using active control. Commun Nonlinear Sci Numer Simul 15(11):3536–3546

    Article  MathSciNet  MATH  Google Scholar 

  13. Mahmoud GM, Mahmoud EE, Arafa AA (2013) Controlling hyperchaotic complex systems with unknown parameters based on adaptive passive method. Chin Phys B 22(6):060508

    Article  Google Scholar 

  14. Sun Z, Zhu W, Si G, Ge Y, Zhang Y (2013) Adaptive synchronization design for uncertain chaotic systems in the presence of unknown system parameters: a revisit. Nonlinear Dyn 72(4):729–749

    Article  MathSciNet  MATH  Google Scholar 

  15. Mahmoud GM, Mahmoud EE (2010) Complete synchronization of chaotic complex nonlinear systems with uncertain parameters. Nonlinear Dyn 62(4):875–882

    Article  MATH  Google Scholar 

  16. Mahmoud EE (2012) Adaptive anti-lag synchronization of two identical or non-identical hyperchaotic complex nonlinear systems with uncertain parameters. J Frankl Inst 349(3):1247–1266

    Article  MathSciNet  MATH  Google Scholar 

  17. Lee TH, Park JH, Lee S, Kwon O (2013) Robust synchronisation of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control. Int J Control 86(1):107–119

    Article  MathSciNet  MATH  Google Scholar 

  18. Ren F, Cao J (2009) Anti-synchronization of stochastic perturbed delayed chaotic neural networks. Neural Comput Appl 18(5):515–521

    Article  MathSciNet  Google Scholar 

  19. Salarieh H, Shahrokhi M (2008) Adaptive synchronization of two different chaotic systems with time varying unknown parameters. Chaos Solitons Fractals 37(1):125–136

    Article  MathSciNet  MATH  Google Scholar 

  20. Cheng Z, Cao J (2011) Synchronization of a growing chaotic network model. Appl Math Comput 218(5):2122–2127

    Article  MathSciNet  MATH  Google Scholar 

  21. Cao J, Li L (2009) Cluster synchronization in an array of hybrid coupled neural networks with delay. Neural Netw 22(4):335–342

    Article  Google Scholar 

  22. Chandrasekar A, Rakkiyappan R, Cao J, Lakshmanan S (2014) Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach. Neural Netw 57:79–93

    Article  MATH  Google Scholar 

  23. Feki M (2003) An adaptive chaos synchronization scheme applied to secure communication. Chaos Solitons Fractals 18(1):141–148

    Article  MathSciNet  MATH  Google Scholar 

  24. Mu X, Pei L (2010) Synchronization of the near-identical chaotic systems with the unknown parameters. Appl Math Model 34(7):1788–1797

    Article  MathSciNet  MATH  Google Scholar 

  25. Senejohnny DM, Delavari H (2012) Active sliding observer scheme based fractional chaos synchronization. Commun Nonlinear Sci Numer Simul 17(11):4373–4383

    Article  MathSciNet  MATH  Google Scholar 

  26. Pourgholi M, Majd VJ (2011) A novel robust proportional-integral (PI) adaptive observer design for chaos synchronization. Chin Phys B 20(12):120503

    Article  Google Scholar 

  27. Nijmeijer H, Mareels IM (1997) An observer looks at synchronization. IEEE Trans Circuits Syst I Fundam Theory Appl 44(10):882–890

    Article  MathSciNet  Google Scholar 

  28. Abdullah A (2013) Synchronization and secure communication of uncertain chaotic systems based on full-order and reduced-order output-affine observers. Appl Math Comput 219(19):10000–10011

    Article  MathSciNet  MATH  Google Scholar 

  29. Bowong S, Moukam Kakmeni F, Fotsin H (2006) A new adaptive observer-based synchronization scheme for private communication. Phys Lett A 355(3):193–201

    Article  MATH  Google Scholar 

  30. Li X, Gu J, Xu W (2013) Adaptive integral observer-based synchronization for chaotic systems with unknown parameters and disturbances. J Appl Math. doi:10.1155/2013/501421

    MathSciNet  MATH  Google Scholar 

  31. Zhang Q (2002) Adaptive observer for multiple-input-multiple-output (MIMO) linear time-varying systems. IEEE Trans Autom Control 47(3):525–529

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Manufacturing Engineering, University of Calgary, 2500 University Dr. NW, Calgary, AB, T2N 1N4, Canada

    P. Bagheri

  2. Department of Chemical and Petroleum Engineering, Sharif University of Technology, P.O. Box 11155-9465, Tehran, Iran

    M. Shahrokhi

Authors
  1. P. Bagheri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Shahrokhi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Shahrokhi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bagheri, P., Shahrokhi, M. Neural network-based synchronization of uncertain chaotic systems with unknown states. Neural Comput & Applic 27, 945–952 (2016). https://doi.org/10.1007/s00521-015-1911-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-015-1911-2

Keywords

Search

Navigation