Skip to main content

Evolutionary and Meta-evolutionary Approach for the Optimization of Chaos Control

  • Conference paper
Swarm and Evolutionary Computation (EC 2012, SIDE 2012)

Abstract

This paper deals with the optimization of control of Hénon Map, which is a discrete chaotic system. This paper introduces and compares evolutionary approach representing tuning of parameters for an existing control method, as well as meta-evolutionary approach representing synthesis of whole control law by means of Analytic Programming (AP). These two approaches are used for the purpose of stabilization of the stable state and higher periodic orbits, which stand for oscillations between several values of chaotic system. For experimentation, Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE) were used.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Senkerik, R., Zelinka, I., Davendra, D., Oplatkova, Z.: Evolutionary Design of Chaos Control in 1D. In: Zelinka, I., Celikovsky, S., Richter, H., Chen, G. (eds.) Evolutionary Algorithms and Chaotic Systems. SCI, vol. 267, pp. 165–190. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  2. Senkerik, R., Zelinka, I., Davendra, D., Oplatkova, Z.: Utilization of SOMA and differential evolution for robust stabilization of chaotic Logistic equation. Computers & Mathematics with Applications 60, 1026–1037 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Zelinka, I., Senkerik, R., Navratil, E.: Investigation on evolutionary optimization of chaos control. Chaos, Solitons & Fractals 40, 111–129 (2009)

    Article  MATH  Google Scholar 

  4. Pyragas, K.: Control of chaos via extended delay feedback. Physics Letters A 206, 323–330 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  5. Pyragas, K.: Continuous control of chaos by self-controlling feedback. Physics Letters A 170, 421–428 (1992)

    Article  Google Scholar 

  6. Just, W.: Principles of Time Delayed Feedback Control. In: Schuster, H.G. (ed.) Handbook of Chaos Control. Wiley-Vch (1999)

    Google Scholar 

  7. Senkerik, R., Oplatkova, Z., Zelinka, I., Davendra, D.: Synthesis of feedback controller for three selected chaotic systems by means of evolutionary techniques: Analytic programming. Mathematical and Computer Modelling (2011), doi:10.1016/j.mcm.2011.05.030

    Google Scholar 

  8. Zelinka, I., Oplatkova, Z., Nolle, L.: Boolean Symmetry Function Synthesis by Means of Arbitrary Evolutionary Algorithms-Comparative Study. International Journal of Simulation Systems, Science and Technology 6, 44–56 (2005)

    Google Scholar 

  9. Zelinka, I.: SOMA – Self Organizing Migrating Algorithm. In: Babu, B., Onwubolu, G. (eds.) New Optimization Techniques in Engineering, ch. 7, p. 33. Springer, Heidelberg (2004)

    Google Scholar 

  10. Zelinka I.: SOMA homepage, http://www.fai.utb.cz/people/zelinka/soma/ (accessed September 22, 2011)

  11. Price, K., Storn, R., Lampinen, J.: Differential Evolution: A Practical Approach to Global Optimization. Natural Computing Series. Springer, Heidelberg (1995)

    Google Scholar 

  12. Price K, Storn R.: Differential evolution homepage, http://www.icsi.berkeley.edu/~storn/code.html (accessed September 22, 2011)

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Senkerik, R., Oplatkova, Z., Davendra, D., Zelinka, I. (2012). Evolutionary and Meta-evolutionary Approach for the Optimization of Chaos Control. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Swarm and Evolutionary Computation. EC SIDE 2012 2012. Lecture Notes in Computer Science, vol 7269. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29353-5_41

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29353-5_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29352-8

  • Online ISBN: 978-3-642-29353-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics