Abstract
This paper proposes a dynamic wavelet network based intelligent adaptive controller design to regulate the chaotic states of the Lorenz equations. The “Dynamic Wavelet Network (DWN)” has lag dynamics, non-orthogonal mother wavelets as activation function and interconnection weights. Adaptation is done by adjusting parameters of the DWN to minimize the cost functional of the Lorenz system operating state errors. The cost gradients with respect to the network parameters are calculated by adjoint sensitivity analysis. It is illustrated in simulations that this control approach is more successful than the previous controllers for eliminating the tracking errors due to the set point changes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Vincent, T.L., Yu, J.: Control of a Chaotic System. Dynamics and Control 1(1), 35–52 (1991)
Yu, X.: Controlling Lorenz Chaos. International Journal of Systems Science 27(4), 355–359 (1996)
Hwang, C.C., Fung, R.F., Hsieh, J.Y., Li, W.J.: A Nonlinear Feedback Control of the Lorenz Equation. International Journal of Engineering Science 37(14), 1893–1900 (1999)
Hartly, T.T., Mossayebi, F.: Classical Control of a Chaotic System. International Journal of Bifurcation and Chaos 2, 881 (1992)
Yeap, T.H., Ahmed, N.U.: Feedback Control of Chaotic Systems. Dynamics and Control 4(1), 97–114 (1994)
Zeng, Y., Singh, S.N.: Adaptive Control of Chaos in Lorenz System. Dynamics and Control 7(2), 143–154 (1997)
Liao, T.H.: Adaptive Synchronization of Two Lorenz Systems. Chaos, Solitons, & Fractals 9(9), 1555–1561 (1998)
Becerikli, Y., Oysal, Y., Konar, A.F.: On a Dynamic Wavelet Network and Its Modeling Application. In: Kaynak, O., Alpaydın, E., Oja, E., Xu, L. (eds.) ICANN 2003 and ICONIP 2003. LNCS, vol. 2714, pp. 710–718. Springer, Heidelberg (2003)
Becerikli, Y., Oysal, Y., Konar, A.F.: Modeling of Nonlinear Systems with Dynamic Wavelet Networks. In: Proc. Turkish Symposium on Automatic Control, Ankara. METU, vol. 1, pp. 71–79 (2002)
Sparrow, C.: The Lorenz Equations. Bifurcations, Chaos and Strange Attractors. Springer, Berlin (1982)
Becerikli, Y., Konar, A.F., Samad, T.: Intelligent Optimal Control with Dynamic Neural Networks. Neural Networks 16, 251–259 (2003)
Mallat, S.: A Theory for Multiresulation Signal Decomposition: the Wavelet Representation. IEEE Trans. On Pattern Analysis and Machine Intelligence 11(7), 674–693 (1989)
Konar, A.F., Samad, T.: Dynamic Neural Networks. Technical Report SSDC-92-I 4152-2, Honeywell Technology Center, 3660 Technology Drive, Minneapolis, MN 55418 (1992)
Chapra, S.C., Canale, R.P.: Numerical Methods for Engineers. McGraw-Hill, Inc., New York (1989)
Edgar, T.F., Himmelblau, D.M.: Optimization of Chemical Processes. McGraw-Hill, New York (1988)
Anderson, J.A., Rosenfeld: Neurocomputing: Foundation of Research. MIT Press, Cambridge (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Oysal, Y. (2004). An Intelligent Control of Chaos in Lorenz System with a Dynamic Wavelet Network. In: Negoita, M.G., Howlett, R.J., Jain, L.C. (eds) Knowledge-Based Intelligent Information and Engineering Systems. KES 2004. Lecture Notes in Computer Science(), vol 3215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30134-9_78
Download citation
DOI: https://doi.org/10.1007/978-3-540-30134-9_78
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23205-6
Online ISBN: 978-3-540-30134-9
eBook Packages: Springer Book Archive