Skip to main content
SpringerLink
Log in

Chaos Control of Lorenz System Using Small Gain Theorem

  • Conference paper
Advances in Neural Networks – ISNN 2009 (ISNN 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5552))

Included in the following conference series:

  • 1346 Accesses

Abstract

This paper studies the problem of controlling chaos in Lorenz system. By dividing Lorenz system into two subsystems, the small gain theorem is used to design linear feedback controllers to make the equilibrium points of the controlled system globally asymptotically stable. Thus chaos in Lorenz system disappears under the controller.

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ott, E., Grebogi, C., Yorke, J.A.: Controlling Chaos. Phys. Rev. Lett. 64, 1196–1199 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  2. Yang, X.S., Zhang, S.C.: On the Possibility of Creating New Asymptotically Stable Periodic Orbits in Continuous Time Dynamical Systems by Small Feedback Control. Nonlinearity 16, 1853–1859 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Wu, T., Chen, M.S.: Chaos Control of the Modified Chua’s Circuit System. Physica. D 164, 53–58 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Yassen, M.T.: Chaos Control of Chen Chaotic Dynamical System. Chaos, Solitons & Fractals 15, 271–283 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, M.Y., Zhou, D.H., Shang, Y.: Nonlinear Feedback Control of Lorenz System. Chaos, Solitons & Fractals 21, 295–304 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Yang, T., Li, X.F., Shao, H.H.: Chaotic Synchronization Using Backstepping Method with Application to the Chua’s Circuit and Lorenz System. In: Proceedings of the American Control Conference, pp. 2299–2300 (2001)

    Google Scholar 

  7. Yang, S., Chen, C., Yan, H.: Control of Chaos in Lorenz System. Chaos, Solitons & Fractals 13, 767–780 (2002)

    Article  MATH  Google Scholar 

  8. Gao, F., Liu, W.Q., Sreeram, V., Teo, K.L.: I Nonlinear Feedback Control for the Lorenz System. Dyn. Control 11(1), 57–69 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bai, E.W., Lonngen, K.E.: Synchronization and Control of Chaotic Systems. Chaos, Solitons & Fractals 10, 1571–1575 (1999)

    Article  Google Scholar 

  10. Lorenz, E.N.: Deterministic Nonperiodic Flow. J. Atmos. Sci. 20, 130–141 (1963)

    Article  Google Scholar 

  11. Chen, G., Ueta, T.: Yet Another Chaotic Attractor. Internat. J. Bifurcation Chaos 9(7), 1465–1466 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lü, J., Chen, G.: A New Chaotic Attractor Coined. Int. J. Bifurcation Chaos 12, 659–661 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  13. Liao, X.X., Luo, H.G., et al.: New Results on Global Synchronization of Chua’s Circuit. Acta Automatica Sinica 31(02), 320–326 (2005)

    Google Scholar 

  14. Isidori, A.: Nonlinear Control Systems II. Springer, London (1999)

    Book  MATH  Google Scholar 

  15. Liu, B., Liu, X.Z., Liao, X.X.: Study for Chaos Synchronization Based on General Lur’e Systems. Acta Automatica Sinica 30(01), 155–160 (2004)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, Hubei University of Economics, Wuhan, 430205, China

    Lei Wang & Jian-Hao Xu

  2. Department of Basic Courses, Public Security Marine Police Academy, Ningbo, 315801, China

    Ti-Biao Wang

Authors
  1. Lei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian-Hao Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ti-Biao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Departamento de Control Automático,, CINVESTAV-IPN,, A.P. 14-740, Av.IPN 2508,, D.F., 07360,, México, México

    Wen Yu

  2. Deptartment of Electrical and Computer Engineering,, Stevens Institute of Technology,, NJ 07030,, Hoboken,, USA

    Haibo He

  3. Dept. of Electrical and Computer Engineering,, South Dakota School of Mines & Technology,, 501 E. St. Joseph Street,, SD 57701,, Rapid City,, USA

    Nian Zhang

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, L., Xu, JH., Wang, TB. (2009). Chaos Control of Lorenz System Using Small Gain Theorem. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01510-6_133

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-01510-6_133

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01509-0

  • Online ISBN: 978-3-642-01510-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation