Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate

Kürşad GÖKCE, (Sakarya Üniversitesi, Fen Bilimleri Enstitüsü, Elektrik ve Elektronik Mühendisliği Anabilim Dalı, Sakarya, Türkiye)
Yılmaz UYAROĞLU (Sakarya Üniversitesi, Mühendislik Fakültesi, Elektrik Elektronik Mühendisliği Bölümü, Sakarya, Türkiye)
Turkish Journal of Electrical Engineering and Computer Sciences
2 0
Yıl: 2013 Cilt: 21 Sayı: 3 Sayfa Aralığı: 793 - 803 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate

Öz:
This paper proposes a feedforward neural network-based control scheme to control the chaotic trajectories of a discrete-H´enon map in order to stay within an acceptable distance from the stable fixed point. An adaptive learning back propagation algorithm with online training is employed to improve the effectiveness of the proposed method. The simulation study carried in the discrete-Henon system verifies the validity of the proposed control system.
Anahtar Kelime:

Konular: Mühendislik, Elektrik ve Elektronik
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] I. Dalkıran, K. Danı¸sman, “Artificial neural network based chaotic generator for cryptology”, Turkish Journal of Electrical Engineering & Computer Sciences, Vol. 18, pp. 225–240, 2010.
  • [2] L. Shilnikov, “Mathematical problems of nonlinear dynamics: a tutorial”, Journal of the Franklin Institute, Vol. 334B, pp. 793–864, 1997.
  • [3] ˙I. Pehlivan, Y. Uyaroglu, “A new chaotic attractor from general Lorenz system family and its electronic experimental implementation”, Turkish Journal of Electrical & Computer Sciences, Vol. 18, pp. 171–184, 2010.
  • [4] R. Kılı¸c, F.Y. Dalkıran, “Programmable design and implementation of a chaotic system utilizing multiple nonlinear functions”, Turkish Journal of Electrical & Computer Sciences, Vol. 18, pp. 647–656, 2010.
  • [5] E. Ott, C. Grebogi, J.A. Yorke, “Controlling chaos”, Physical Review Letters, Vol. 64, pp. 1196–1199, 1990.
  • [6] C. Grebogi, “Control and applications of chaos”, Journal of the Franklin Institute, Vol. 334B, pp. 1115–1146, 1997.
  • [7] Y.P. Tian, X. Yu, “Stabilizing unstable periodic orbits of chaotic systems via an optimal principle”, Journal of the Franklin Institute, Vol. 337, pp. 771–779, 2000.
  • [8] C. Hernandez, J. Castellanos, R. Gonzalo, V. Palencia, “Neural control of chaos and applications”, International Journal on Information Theory and Applications, Vol. 12, pp. 103–110, 2008.
  • [9] A. Castellanos, R. Gonzalo, A. Martinez, “Simultaneous control of chaotic systems using RBF networks”, 6th International Conference on Information Research and Applications, 2008.
  • [10] Z. Yang, Q. Yao, C. Yang,, “Control and synchronization of H´enon chaos via a novel variable structure control”, Dynamics of Continuous, Discrete and Impulsive Systems Series B, Vol. 11, pp. 665–672, 2004.
  • [11] S.V. Kamarthi, S. Pittner, “Accelerating neural network training using weight extrapolations”, Neural Networks, Vol. 12, pp. 1285–1299, 1999.
  • [12] L. dos Santos Coelho, D.L. de Andrade Bernert, “An improved harmony search algorithm for synchronization of discrete-time chaotic systems”, Chaos, Solitons and Fractals, Vol. 41, pp. 2526–2532, 2009.
  • [13] J.A.K. Suykens, J. Vandewalle, “Chaos control using least-squares support vector machines”, International Journal of Circuit Theory and Applications, Vol. 27, pp. 605–615, 1999.
  • [14] X.P. Zong, Y. Geng, “Control chaotic systems based on BP neural network with a new perturbation”, International Conference on Wavelet Analysis and Pattern Recognition, pp. 166–170, 2009.
  • [15] M.P. Alsing, R. Gavrielides, V. Kovanis, “Controlling unstable periodic orbits in a nonlinear optical system: the Ikeda map”, Nonlinear Optics: Materials, Fundamentals and Applications, pp. 72–74, 1994.
  • [16] C. Hernandez, A. Martinez, J. Castellanos, F.L Mingo, “Controlling chaotic nonlinear dynamical systems”, Proceedings of the 6th IEEE International Conference on Electronics, Circuits and Systems,, Vol. 3, pp. 1231–1234, 1999.
  • [17] M. Henon, “A two-dimensional mapping with a strange attractor”, Communications in Mathematical Physics, Vol. 50, pp. 69–77, 1976.
  • [18] C. Murakami, W. Murakami, K. Hirose, “Sequence of global period doubling bifurcation in the H´enon maps”, Chaos, Solitons and Fractals, Vol. 14, pp. 1–17, 2002.
  • [19] L.M. Saini, “Peak load forecasting using Bayesian regularization resilient and adaptive back propagation learning based artificial neural networks”, Electric Power Systems Research, Vol. 78, pp. 1302–1310, 2008.
APA GÖKCE K, Uyaroglu Y (2013). Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate. , 793 - 803.
Chicago GÖKCE Kürşad,Uyaroglu Yılmaz Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate. (2013): 793 - 803.
MLA GÖKCE Kürşad,Uyaroglu Yılmaz Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate. , 2013, ss.793 - 803.
AMA GÖKCE K,Uyaroglu Y Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate. . 2013; 793 - 803.
Vancouver GÖKCE K,Uyaroglu Y Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate. . 2013; 793 - 803.
IEEE GÖKCE K,Uyaroglu Y "Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate." , ss.793 - 803, 2013.
ISNAD GÖKCE, Kürşad - Uyaroglu, Yılmaz. "Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate". (2013), 793-803.
APA GÖKCE K, Uyaroglu Y (2013). Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate. Turkish Journal of Electrical Engineering and Computer Sciences, 21(3), 793 - 803.
Chicago GÖKCE Kürşad,Uyaroglu Yılmaz Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate. Turkish Journal of Electrical Engineering and Computer Sciences 21, no.3 (2013): 793 - 803.
MLA GÖKCE Kürşad,Uyaroglu Yılmaz Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate. Turkish Journal of Electrical Engineering and Computer Sciences, vol.21, no.3, 2013, ss.793 - 803.
AMA GÖKCE K,Uyaroglu Y Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate. Turkish Journal of Electrical Engineering and Computer Sciences. 2013; 21(3): 793 - 803.
Vancouver GÖKCE K,Uyaroglu Y Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate. Turkish Journal of Electrical Engineering and Computer Sciences. 2013; 21(3): 793 - 803.
IEEE GÖKCE K,Uyaroglu Y "Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate." Turkish Journal of Electrical Engineering and Computer Sciences, 21, ss.793 - 803, 2013.
ISNAD GÖKCE, Kürşad - Uyaroglu, Yılmaz. "Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate". Turkish Journal of Electrical Engineering and Computer Sciences 21/3 (2013), 793-803.
Sayfa Oluşturulma Tarihi
22-04-2024 18:41

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