Skip to main content
SpringerLink
Log in

Minimum Time Synchronization of Chaotic Systems via Numerical Optimal Control Techniques

  • Conference paper
  • First Online:
Optimization and Control Techniques and Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 86))

  • 1140 Accesses

Abstract

Chaos synchronization has attracted much attention in recent decades since it has not only brought theoretical challenges but also could be applied to many real-world applications, such as digital communication, complex networks, and semiconductor lasers communication systems. We consider the minimum time problem of chaos synchronization via optimal control computation. The general synchronization scheme consists of identical/non-identical drive and response chaotic systems. We propose a novel computational approach to compute the minimum synchronization time of the drive-response chaotic systems and the corresponding optimal controls in a finite time horizon. By the control parametrization technique, the minimum-time chaos synchronization problem is transformed to an optimal parameter selection problem in two stages. A computational synchronization algorithm is hence devised to compute the minimum synchronization time and the optimal controls. For illustration, an exemplary scheme of Lorenz–Rossler chaotic systems is given to demonstrate the effectiveness of the proposed algorithm.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

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

    Article  Google Scholar 

  2. Celikovsky, S., Chen, G.R.: Secure synchronization of a class of chaotic systems from a nonlinear observer approach. IEEE Trans. Autom. Control 50, 76–82 (2005)

    Article  MathSciNet  Google Scholar 

  3. Chen, H.H.: Global synchronization of chaotic systems via linear balanced feedback control. Appl. Math. Comput. 186, 923–931 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chen, M.Y.: Chaos synchronization in complex networks. IEEE Trans. Circuits Syst. I Regul. Pap. 55, 1335–1346 (2008)

    Article  MathSciNet  Google Scholar 

  5. Hu, G.J., Feng, Z.J., Meng, R.L.: Chosen ciphertext attack on chaos communication based on chaotic synchronization. IEEE Trans. Circuits Syst. I Fundam. Theor. Appl. 50, 275–279 (2003)

    Article  Google Scholar 

  6. Jennings, L.S., Fisher, M.E., Teo, K.L., Goh, C.J.: MISER3 Optimal Control Software: Theory and User Manual. EMCOSS Pty. Ltd, Perth (1990)

    Google Scholar 

  7. Jiang, G.P., Zheng, W.X., Tang, W.K.S., Chen, G.R.: Integral-observer-based chaos synchronization. IEEE Trans. Circuits Syst. II Express Briefs 53, 110–114 (2006)

    Article  Google Scholar 

  8. Kolumban, G., Kennedy, M.P.: The role of synchronization in digital communications using chaos—part III: performance bounds for correlation receivers. IEEE Trans. Circuits Syst. I Fundam. Theor. Appl. 47, 1673–1683 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  9. Liu, Y., Chen, M.F., Liu, J.M., Davis, P., Aida, T.: Communication using synchronization of optical-feedback-induced chaos in semiconductor lasers. IEEE Trans. Circuits Syst. I Fundam. Theor. Appl. 48, 1484–1490 (2001)

    Article  Google Scholar 

  10. Liang, X., Zhang, J., Xia, X.: Adaptive synchronization for generalized Lorenz systems. IEEE Trans. Autom. Control 53, 1740–1746 (2008)

    Article  MathSciNet  Google Scholar 

  11. Lu, J., Cao, J., Ho, D.: Adaptive stabilization and synchronization for chaotic Lure systems with time-varying delay. IEEE Trans. Circuits Syst. I Fundam. Theor. Appl. 55, 1347–1356 (2008)

    Article  MathSciNet  Google Scholar 

  12. Lu, J., Hill, D.J.: Global asymptotical synchronization of chaotic Lur’e systems using sampled data: a linear matrix inequality approach. IEEE Trans. Circuits Syst. II Express Briefs 55, 586–590 (2006)

    Google Scholar 

  13. Rossler, O.E.: An equation for continuous chaos. Phys. Lett. A 57, 397–398 (1976)

    Article  Google Scholar 

  14. Teo, K.L.: A unified computational approach to optimal control problem. In: Lakshmikantham, V. (ed.) World Congress of Nonlinear Analysts’92, pp. 763–2774. Walter de ruyter, Berlin, New York (1996)

    Google Scholar 

  15. Teo, K.L., Goh, C.J., Wong, K.H.: A Unified Computational Approach to Optimal Control Problems. Longman, New York (1991)

    MATH  Google Scholar 

  16. Volkovskii, A.: Synchronization of chaotic systems using phase control. IEEE Trans. Circuits Syst. I Fundam. Theor. Appl. 44, 913–917 (1997)

    Article  MathSciNet  Google Scholar 

  17. Yassen, M.T.: Chaos synchronization between two different chaotic systems using active control. Chaos Soliton. Fract. 23, 131–140 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  18. Yassen, M.T.: Adaptive control and synchronization of a modified Chua’s circuit system. Appl. Math. Comput. 135, 113–128 (2003)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China (No. 11171079, No. 61290325), HUST Startup Research Fund, HUST Independent Innovation Research Fund (GF and Natural Science) and the ARC Discovery Project under grant DP110102855.

Author information

Authors and Affiliations

  1. School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, China

    Honglei Xu

  2. Department of Mathematics and Statistics, Curtin University, Perth, Australia

    Honglei Xu, Guanglu Zhou & Louis Caccetta

Authors
  1. Honglei Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guanglu Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Louis Caccetta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Honglei Xu .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, Curtin University, Perth, West Australia, Australia

    Honglei Xu

  2. Department of Mathematics and Statistics, Curtin Univeristy, Perth, Australia

    Kok Lay Teo

  3. Department of Mathematics, China University of Petroleum, Beijing, China

    Yi Zhang

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Xu, H., Zhou, G., Caccetta, L. (2014). Minimum Time Synchronization of Chaotic Systems via Numerical Optimal Control Techniques. In: Xu, H., Teo, K., Zhang, Y. (eds) Optimization and Control Techniques and Applications. Springer Proceedings in Mathematics & Statistics, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43404-8_8

Download citation

Publish with us

Policies and ethics

Search

Navigation