Applied Intelligence

, Volume 45, Issue 3, pp 793–807 | Cite as

Design of an intelligent prediction-based neural network controller for multi-scroll chaotic systems

Article

Abstract

An indispensable part of the precise control of multi-scroll chaotic systems, model identification has received increasing attention in recent years. Because of plant uncertainty and unmodeled dynamics, conventional control methods cannot guarantee a sufficiently high-performance for stabilizing multi-scroll chaotic systems. In an effort to tackle the matter better, we propose an intelligent controller called the adaptive neural network prediction-based controller (NN-PbC ). The specified neural network is trained with the system model, which is extracted from a time series. In actual practice, the data are divided into two sets. One set is used for training and the other set for testing. In fact, a generalized NN will perform well for both training and testing data. The prediction-based control method is then applied to the obtained neural network model to stabilize the multiple equilibrium points. The stability of the closed-loop system is proven. In addition, simulation examples on two typical multi-scroll chaotic systems are presented to demonstrate the effectiveness of the proposed controller.

Keywords

Adaptive neural network Multi-scroll chaotic systems Prediction-based control System identification 

Notes

Acknowledgments

The work described in this paper is supported by the DGRSDT (Direction Générale de la Recherche Scientifique et du Développement Technologique) of Algeria Grant N D01720130025. The authors also gratefully acknowledge the helpful comments and suggestions of the anonymous reviewers that have improved the quality of the paper.

References

  1. 1.
    Ott E (1993) Chaos in dynamical systems. Cambridge University Press, CambridgeMATHGoogle Scholar
  2. 2.
    Kapitaniak T (2000) Chaos for engineers theory applications and control, 2nd edn. Springer, BerlinMATHGoogle Scholar
  3. 3.
    Banerjee S, Mitra M, Rondoni L (2011) Applications of chaos and nonlinear dynamics in engineering, vol 1. Springer, BerlinCrossRefMATHGoogle Scholar
  4. 4.
    Banerjee S, Rondoni L, Mitra M (2014) Applications of chaos and nonlinear dynamics in science and engineering, vol 2. Springer, BerlinGoogle Scholar
  5. 5.
    Suykens JA, Vandewalle J (1993) Generation of n-double scrolls (n = 1, 2, 3, 4, …). IEEE Trans Circuits Syst I 40(11):861–867CrossRefMATHGoogle Scholar
  6. 6.
    Tang KS, Zhong GQ, Chen G, Man KF (2001) Generation of n-scroll attractors via sine function. IEEE Trans Circuits Syst I 48:1369–1372MathSciNetCrossRefGoogle Scholar
  7. 7.
    Yalcin ME, Suykens JAK, Vandewalle J, Ozoguz S (2002) Families of scroll grid attractors. Int J Bifurcat Chaos 12:23–41MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Lin Y, Wang C, He H (2015) A simple multi-scroll chaotic oscillator employing CCIIs. Int J Light Electron Opt 126:824–827CrossRefGoogle Scholar
  9. 9.
    Han F, Yu X, Wang Y, Feng Y, Chen G (2003) N-scroll chaotic attractors by second-order system and double hysteresis blocks. Electron Lett 39:1636–1637CrossRefGoogle Scholar
  10. 10.
    Elwakil AS, Ozoguz S (2006) Multi-scroll chaotic attractors: the non autonomous approach. IEEE Trans Circuits Syst II 53:862–866CrossRefGoogle Scholar
  11. 11.
    Lü J, Chen G (2006) Generating multi-scroll chaotic attractors: theories, methods and applications. Int J Bifurcat Chaos 16:775–858CrossRefGoogle Scholar
  12. 12.
    Lü J, Murali K, Sinha S, Leung H, Aziz-Alaoui MA (2008) Generating multi-scroll chaotic attractors by thresholding. Phys Lett A 372:3234–3239CrossRefMATHGoogle Scholar
  13. 13.
    Wang L, Yang X, Vandewalle J, Ozoguz S (2006) Generation of multi-scroll delayed chaotic oscillator. Electron Lett 42:1439–1441CrossRefGoogle Scholar
  14. 14.
    Zhang C, Yu S (2010) Generation of grid multi-scroll chaotic attractors via switching piecewise linear controller. Phys Lett A 374:3029–3037CrossRefMATHGoogle Scholar
  15. 15.
    Liu X, Shen X, Zhang H (2012) Multi-scroll chaotic and hyperchaotic attractors generated from Chen system. Int J Bifurcat Chaos 22:1250033CrossRefMATHGoogle Scholar
  16. 16.
    Ma Y, Li Y, Jiang X (2015) Simulation and circuit implementation of 12-scroll chaotic system. Chaos Solit Fract 75:127–133MathSciNetCrossRefGoogle Scholar
  17. 17.
    Tlelo-Cuautle E, Rangel-Magdaleno JJ, Pano-Azucena AD, Obeso-Rodelo PJ, Nunez-Perez JC (2015) FPGA realization of multi-scroll chaotic oscillators. Commun Nonlinear Sci Numer Simul 27:66–80MathSciNetCrossRefGoogle Scholar
  18. 18.
    Xu F, Yu P (2010) Chaos control and chaos synchronization for multi-scroll chaotic attractors generated using hyperbolic functions. J Math Anal Appl 362:252–274MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Ahmad WM (2005) Generation and control of multi-scroll chaotic attractors in fractional order systems. Chaos Solitons Fractals 25:727–735CrossRefMATHGoogle Scholar
  20. 20.
    Boukabou A, Sayoud B, Boumaiza H, Mansouri N (2009) Control of n-scroll Chua’s circuit. Int J Bifurcat Chaos 19:3813–3822CrossRefMATHGoogle Scholar
  21. 21.
    Hadef S, Boukabou A (2014) Control of multi-scroll Chen system. J Franklin Inst 351:2728–2741MathSciNetCrossRefGoogle Scholar
  22. 22.
    Pham D, Liu X (1995) Neural networks for identification, prediction and control. Springer, LondonCrossRefGoogle Scholar
  23. 23.
    Haykin S (1999) Neural networks: a comprehensive foundation, 2nd edn. Prentice-Hall, Englewood CliffsMATHGoogle Scholar
  24. 24.
    Weeks ER, Burgess JM (1997) Evolving artificial neural networks to control chaotic systems. Phys Rev E 56:1531–1540CrossRefGoogle Scholar
  25. 25.
    Kuo JM, Principe JC, de Vries B (1992) Prediction of chaotic time series using recurrent neural networks. In: IEEE workshop neural networks for signal processing, pp 436–443Google Scholar
  26. 26.
    Poznyak AS, Yu W, Sanchez EN (1999) Identification and control of unknown chaotic systems via dynamic neural networks. IEEE Trans Circuits Syst I 46:1491–1495CrossRefMATHGoogle Scholar
  27. 27.
    Yadmellat P, Nikravesh SKY (2011) A recursive delayed output-feedback control to stabilize chaotic systems using linear-in-parameter neural networks. Commun Nonlinear Sci Numer Simul 16:383–394MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Lu Z, Shieh LS, Chen G, Coleman NP (2006) Adaptive feedback linearization control of chaotic systems via recurrent high-order neural networks. Inf Sci 176:2337–2354MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Khelifa MA, Boukabou A (2014) Control of UPOs of unknown chaotic systems via ANN. In: Proceedings of the 24th international conference on artificial neural networks and learning machines, pp 627–634Google Scholar
  30. 30.
    Hsu CF (2012) Adaptive dynamic CMAC neural control of nonlinear chaotic systems with L 2 tracking performance. Eng Appl Artif Intell 25997–1008Google Scholar
  31. 31.
    Hsu CF (2014) Intelligent control of chaotic systems via self-organizing Hermite-polynomial-based neural network. Neurocomputing 123:197–206CrossRefGoogle Scholar
  32. 32.
    Qin W, Yang Y, Zhang J (2009) Controlling the chaotic response to a prospective external signal using back-propagation neural networks. Nonlinear Anal Real World Appl 10:2985–2989MathSciNetCrossRefMATHGoogle Scholar
  33. 33.
    Türk M, Oğraş H (2010) Recognition of multi-scroll chaotic attractors using wavelet-based neural network and performance comparison of wavelet families. Expert Syst Appl 37:8667–8672CrossRefGoogle Scholar
  34. 34.
    Türk M, Gülten A (2011) Modelling and simulation of the multi-scroll chaotic attractors using bond graph technique. Simul Model Pract Theory 19:899–910CrossRefGoogle Scholar
  35. 35.
    Boukabou A, Chebbah A, Mansouri N (2008) Predictive control of continuous chaotic systems. Int J Bifurcat Chaos 18:587–592CrossRefGoogle Scholar
  36. 36.
    Senouci A, Boukabou A (2014) Predictive control and synchronization of chaotic and hyperchaotic systems based on a T-S fuzzy model. Math Comput Simul 105:62–78MathSciNetCrossRefGoogle Scholar
  37. 37.
    Zheng Y (2015) Fuzzy prediction-based feedback control of fractional order chaotic systems. Int J Light Electron Optics 126:5645–5649CrossRefGoogle Scholar
  38. 38.
    Grüne L, Pannek J (2011) Nonlinear model predictive control: theory and algorithms. Springer, LondonCrossRefMATHGoogle Scholar
  39. 39.
    Ushio T, Yamamoto S (1999) Prediction-based control of chaos. Phys Lett A 264:30–35MathSciNetCrossRefMATHGoogle Scholar
  40. 40.
    Khalil H (2002) Nonlinear systems. Prentice Hall, New JerseyMATHGoogle Scholar
  41. 41.
    Barron AR (1993) Universal approximation bounds for superposition of a sigmoidal function. IEEE Trans Inform Theory 39:930–945MathSciNetCrossRefMATHGoogle Scholar
  42. 42.
    Draper N, Smith H (1981) Applied linear regression, 2nd edn. Wiley, New YorkMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of ElectronicsJijel UniversityJijelAlgeria

Personalised recommendations