Application of Analytic Programming for Evolutionary Synthesis of Control Law—Introduction of Two Approaches

  • Roman Šenkeřík
  • Zuzana Oplatková
  • Ivan Zelinka
  • Roman Jašek
Part of the Studies in Computational Intelligence book series (SCI, volume 416)

Abstract

This research deals with an evolutionary synthesis of control law for Logistic equation, which is a discrete chaotic system. The novelty of the research is that an Analytic Programming (AP), which is a tool for symbolic regression, is used for the synthesis of feedback controller for chaotic system. This work introduces and compares two approaches representing blackbox type cost function, as well as not-blackbox type cost function. These two approaches are used for the purpose of stabilisation of the higher periodic orbits, which stand for oscillations between several values of chaotic system. The work consists of the descriptions of analytic programming as well as chaotic system and used cost functions. For experimentation, Self-Organising Migrating Algorithm (SOMA) and Differential Evolution (DE) were used.

Keywords

Cost Function Periodic Orbit Differential Evolution Chaotic System Chaos Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Coelho, L.D.: Self-organizing migrating strategies applied to reliability-redundancy optimization of systems. IEEE Transactions on Reliability 58(3), 501–510 (2009)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Coelho, L.D.: Self-organizing migration algorithm applied to machining allocation of clutch assembly. Mathematics and Computers in Simulation 80(2), 427–435 (2009)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Coelho, L.D., Mariani, V.C.: An efficient cultural self-organizing migrating strategy for economic dispatch optimization with valve-point effect. Energy Conversion and Management 51(12), 2580–2587 (2010)CrossRefGoogle Scholar
  4. 4.
    Davendra, D., Zelinka, I., Senkerik, R.: Chaos driven evolutionary algorithms for the task of pid control. Computers & Mathematics with Applications 60(4), 1088–1104 (2010)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Hilborn, R.C.: Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers. Oxford University Press (2000)Google Scholar
  6. 6.
    Just, W.: Principles of time delayed feedback control. In: Schuster, H.G. (ed.) Handbook of Chaos Control. Wiley-Vch (1999)Google Scholar
  7. 7.
    Lampinen, J., Zelinka, I.: New ideas in optimization. In: Mechanical Engineering Design Optimization by Differential Evolution. McGraw-Hill (1999)Google Scholar
  8. 8.
    May, R.M.: Stability and Complexity in Model Ecosystems. Princeton University Press (2001)Google Scholar
  9. 9.
    Oplatkova, Z., Zelinka, I.: Investigation on evolutionary synthesis of movement commands. Modelling and Simulation in Engineering (2009)Google Scholar
  10. 10.
    Price, K., Storn, R.M.: Differential evolution homepage, http://www.icsi.berkeley.edu/~storn/code.html (accessed September 30, 2011)
  11. 11.
    Price, K., Storn, R.M., Lampinen, J.A.: Differential evolution: A practical approach to global optimization. Natural Computing Series. Springer (1995)Google Scholar
  12. 12.
    Pyragas, K.: Continuous control of chaos by self-controlling feedback. Physics Letters A 170, 421–428 (1992)CrossRefGoogle Scholar
  13. 13.
    Pyragas, K.: Control of chaos via extended delay feedback. Physics Letters A 2006 (1995)Google Scholar
  14. 14.
    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 (2010), doi:10.1016/j.mcm.2011.05.030Google Scholar
  15. 15.
    Senkerik, R., Oplatkova, Z., Zelinka, I., Davendra, D., Jasek, R.: Evolutionary synthesis of control law for higher periodic orbits of chaotic logistic equation. In: 25th European Conference on Modelling and Simulation. European Council for Modelling and Simulation, pp. 452–458 (2011)Google Scholar
  16. 16.
    Senkerik, R., Oplatkova, Z., Zelinka, I., Davendra, D., Jasek, R.: Synthesis of feedback control law for stabilization of chaotic system oscillations by means of analytic programming — preliminary study. In: 5th Global Conference on Power Control and Optimization (2011)Google Scholar
  17. 17.
    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)CrossRefGoogle Scholar
  18. 18.
    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(4), 1026–1037 (2010)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Zelinka, I.: Soma — self organizing migrating algorithm. In: Babu, B., Onwubolu, G. (eds.) New Optimization Techniques in Engineering. Springer (2004)Google Scholar
  20. 20.
    Zelinka, I.: Soma homepage, http://www.fai.utb.cz/people/zelinka/soma/ (accessed September 30, 2011)
  21. 21.
    Zelinka, I., Davendra, D., Senkerik, R., Jasek, R., Oplatkova, Z.: Analytical programming — a novel approach for evolutionary synthesis of symbolic structures. In: Kita, E. (ed.) Evolutionary Algorithms. InTech (2011)Google Scholar
  22. 22.
    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(9), 44–56 (2005)Google Scholar
  23. 23.
    Zelinka, I., Senkerik, R., Navratil, E.: Investigation on evolutionary optimization of chaos control. Chaos, Solutions & Fractals 40(1), 111–129 (2009)MATHCrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2012

Authors and Affiliations

  • Roman Šenkeřík
    • 1
  • Zuzana Oplatková
    • 1
  • Ivan Zelinka
    • 2
  • Roman Jašek
    • 1
  1. 1.Faculty of Applied InformaticsTomas Bata University in ZlínZlínCzech Republic
  2. 2.Faculty of Electrical Engineering and Computer ScienceTechnical University of OstravaOstrava-PorubaCzech Republic

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