Intelligent Chaos Controller

A Computational Intelligence Based Approach for Data-Driven Real-World Systems
  • Jallu Krishnaiah
  • C. S. Kumar
  • M. A. Faruqi
Conference paper
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 132)

Abstract

Recent developments have shown the possibility of constructing Bifurcation Diagrams for real-world chaotic system based on observed data. In the present work we demonstrate how the control can be achieved on the data-driven process/system based on the bifurcation diagram construction capability. In reality many physical and non-physical systems are very difficult to represent using a mathematical form; even if mathematical models exist, it would be a difficult task to build a controller which works in real-time. Moreover, if the considered system is chaotic in nature there are very few methods for are available controlling. On contrary there are large number of Chaos Control techniques when the considered system is/has a mathematical model. Based on the fundamental idea of these techniques, i.e. small perturbation at appropriate time is enough to control such a chaotic systems, the present method uses the global search capability of genetic algorithms to find a best perturbation to the control parameter at each step with a RNN model of the considered system as an objective function.

Keywords

Chaotic System Bifurcation Diagram Model Predictive Control Recurrent Neural Network Chaotic Region 
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.
    Fradkov, A.L., Evans, R.J.: Control of chaos: Survey 1997-2000. In: Preprints of 15th IFAC World Congress on Automatic Control. Plenary papers, Survey papers, Milestones, Barcelona, pp. 143–154 (July 2002)Google Scholar
  2. 2.
    Almeida, L.: Backpropagation in perceptrons with feedback. In: Eckmiller, R., der Malsburg, V. (eds.) Neural Computers, pp. 199–208. Springer, New York (1988)Google Scholar
  3. 3.
    Bengio, Y., Gingras, F.: Recurrent neural networks for missing or asynchronous data. In: Neural Information Proceesing Systems. MIT Press (1996)Google Scholar
  4. 4.
    Horne, B.G., Giles, C.: An experimental comparison of recurrent neural networks. In: Advances in Neural Information Processing Systems, p. 697. MIT Press (1995)Google Scholar
  5. 5.
    Boccaletti, S., Grebogi, C., Lai, Y.C., Mancini, H., Maza, D.: The control of chaos: Theory and applications. Physics Reports 329(3), 103–197 (2000)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Andrievskii, B.R., Fradkov, A.L.: Control of chaos: Methods and applications. 2.applications. Automation and Remote Control 65(4), 505–533 (2003)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Hilborn, R.C.: Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers, 2nd edn. Oxford University Press, New York (2000)MATHGoogle Scholar
  8. 8.
    Christini, D.J., Collins, J.J.: Controlling neuronal chaos using chaos control, http://arxiv.org/abs/chao-dyn/9503003
  9. 9.
    Dattani, J., Blake, J.C., Hilker, F.M.: Target-oriented chaos control. Physics Letters A 375(45), 3986–3992 (2011), http://www.sciencedirect.com/science/article/pii/S0375960111011194 CrossRefGoogle Scholar
  10. 10.
    De Feo, O.: Self-emergence of chaos in the identification of irregular periodic behaviour. CHAOS 13(4), 1205–1215 (2003)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Doya, K.: Bifurcations in the learning of recurrent neural networks. In: Proc. IEEE Int. Symp. Circuits and Systems, pp. 2777–2780. IEEE (1992)Google Scholar
  12. 12.
    Elman, J.: Finding structure in time. Cognitive Science 6(2), 285–324 (1990)Google Scholar
  13. 13.
    Jones, A.J., Tsui, A., Oliveira, A.G.: Neural models of arbitrary chaotic systems: construction and the role of time delayed feedback in control and synchronization. Complexity International 9 (2002)Google Scholar
  14. 14.
    Aihara, K., Takabe, T., Toyoda, M.: Chaotic neural networks. Special Issue on Recurrent Networks for Sequence Processing 144(12), 333–340 (1990)MathSciNetGoogle Scholar
  15. 15.
    Krishnaiah, J., Kumar, C., Faruqi, M.A.: Modelling and control of chaotic processes through their bifurcation diagrams generated with the help of recurrent neural networks models: Part 1 - simulation studies. Journal of Process Control 16(1), 53–66 (2006)CrossRefGoogle Scholar
  16. 16.
    Kuo, J.M., Principe, J.C., de Vries, B.: Prediction of chaotic time-series using recurrent neural networks. Submitted to IEEE Workshop NN for SP (1992)Google Scholar
  17. 17.
    Fradkov, A.L., Evans, R.J.: Control of chaos: Survey 1997-2000. Survey paper. Univ. of Melbourne, St. Petersburg (2002)Google Scholar
  18. 18.
    Nayfeh, A.H., Balachandran, B.: Applied Nonlinear Dynamics: Analytical, Computational and Experimental Methods. John Willey and Sons, New York (1995)CrossRefMATHGoogle Scholar
  19. 19.
    de Oliveira, A.G., Tsui, A.P., Jones, A.J.: Using a neural network to calculate the sensitivity vectors in synchronisation of chaotic maps. In: Proceedings 1997 International Symposium on Nonlinear Theory and its Applications (NOLTA 1997), vol. 1, pp. 46–49. Research Society of Nonlinear Theory and its Applications, IEICE, Honolulu, U.S.A (1997)Google Scholar
  20. 20.
    Ott, E., Grebogi, C., Yorke, J.A.: Controlling of chaos. Phys. Rev. Lett. 64, 1192–1196 (1990)Google Scholar
  21. 21.
    Ott, E.: Chaos in Dynamical Systems. Cambridge University Press, Maryland (1993)MATHGoogle Scholar
  22. 22.
    Panzyak, A., Yu, W., Sanchez, E.: Identification and control of unknown chaotic systesm via dynamical neural networks. IEEE Trans. on Circuits and Systems 46(12), 1491–1495 (1999)CrossRefGoogle Scholar
  23. 23.
    Pineda, F.J.: Generalization of backpropagation to recurrent neural networks. Physical Review Letters 19, 2229–2232 (1987)CrossRefMathSciNetGoogle Scholar
  24. 24.
    Tsui, A.P.M., Jones, A.J.: Periodic response to external stimulation of a chaotic neural network with delayed feedback. Int. J. of Bifurcation and Chaos 9(4), 713–722 (1999)CrossRefMATHGoogle Scholar
  25. 25.
    Po-Feng, Chu, J.Z., Jang, S.S., Shieh, S.S.: Developing a robust model predictive control architecture through regional knowledge analysis of artificial neural networks. Journal of Process Control 13, 423–435 (2002)Google Scholar
  26. 26.
    Pyragas, K.: Continuous control of chaos by self-controlling feedback. Physics Letters A 170, 421–428 (1992)CrossRefGoogle Scholar
  27. 27.
    Rohwer, R., Forrest, B.: Training time-dependence in neural networks. In: Proceedings of the First IEEE International Conference on Neural Networks, San Diego, CA, vol. 2, pp. 701–708 (1987)Google Scholar
  28. 28.
    Schenk-Hoppé, K.R.: Bifurcations of the randomly perturbed logistic map - numerical study and visualizations, http://www.iew.unizh.ch/home/klaus/logistic/intro.html
  29. 29.
    Schöll, E.: Neural control: Chaos control sets the pace. Nature Physics (2010)Google Scholar
  30. 30.
    Lin, T., Horne, B.G., Tino, P., Giles, C.: Learning long–term dependencies in narx recurrent neural networks. IEEE Trans. on Neural Networks 7(6), 1329 (1996)CrossRefGoogle Scholar
  31. 31.
    Weeks, E.R., Burgess, J.M.: Evolving artificial neural networks to control chaotic systems. Physical Review E 56(2), 1531–1540 (1997)CrossRefGoogle Scholar
  32. 32.
    Ditto, W.L., Rauseo, S.N., Spano, M.L.: Experimental control of chaos. Phys. Rev. Lett. 65(26), 3211–3214 (1990)CrossRefGoogle Scholar
  33. 33.
    Bengio, Y., Simard, P., Frasconi, P.: Learning long-term dependencies with gradient is difficult. IEEE Transactions on Neural Networks 5(2), 157–166 (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jallu Krishnaiah
    • 1
  • C. S. Kumar
    • 2
  • M. A. Faruqi
    • 3
  1. 1.R&D, BHELTrichyIndia
  2. 2.Robotics and Intelligent Systems LabIIT KharagpurIndia
  3. 3.Azad Instistitute of Engineering and TechnologyLucknowIndia

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