Identifying chaotic systems using Wiener and Hammerstein cascade models. (English) Zbl 0992.37074

It is known that in analyzing and synthesizing artificial neural networks (ANNs) one of the difficulties arises from the fact that memory and nonlinearity are intermixed. This paper deals with how to handle this situation. The authors propose two approaches, whereby the nonlinearity and the memory are in a sense separated. These two identification methods have similar functional structures, where a linear dynamic plant is cascaded with a neural network in different orders, called the Wiener and Hammerstein models, respectively.


37M10 Time series analysis of dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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[1] Chen, G., Controlling Chaos and Bifurcations in Engineering Systems (1999), CRC Press: CRC Press Boca Raton, FL
[2] Chen, G.; Dong, X., From chaos to order—Perspectives and methodologies in controlling chaotic nonlinear dynamical systems, Int’l. J. of Bifurcation and Chaos, 3, 1363-1410 (1993) · Zbl 0886.58076
[3] Ogorzalek, M. J., Taming chaos: Part I, Synchronization, Part II, Control, IEEE Trans. on Circ. Sys. I, 40, 693-706 (1993) · Zbl 0850.93353
[4] Chen, G.; Moiola, J. L., An overview of bifurcation, chaos and nonlinear dynamics in control system, J. of Franklin Institute, 331B, 819-858 (1994) · Zbl 0825.93303
[5] Chen, G.; Dong, X., On feedback control of chaotic nonlinear dynamical systems, Int. J. of Bifur. Chaos, 2, 407-411 (1992) · Zbl 0875.93176
[6] Chen, G.; Lai, D., Making a dynamical system chaotic: Feedback control of Lyapunov exponents for discrete-time dynamical system, Int. J. Bifur. Chaos, 6, 1341-1349 (1996) · Zbl 0875.93157
[7] Shinbrot, T.; Grebogi, C.; Ott, E.; Yorke, J. A., Using small perturbations to control chaos, Nature, 363, 411-417 (1993)
[8] Chen, G.; Dong, X., From Chaos to Order: Methodologies, Perspectives and Applications (1998), World Scientific: World Scientific Singapore · Zbl 0908.93005
[9] Qammar, H. K.; Mossayebi, F., System identification and model-based control of a chaotic system, Int. J. of Bifur. Chaos, 4, 843-851 (1994) · Zbl 0875.93077
[10] Carroll, T. L.; Pecora, L. M., Synchronizing chaotic circuits, IEEE Trans. on Circ. Sys., 38, 453-456 (1991)
[11] Chen, G., (Representation, Approximation, and identification, The Circuits and Filters Handbook (1994), CRC Press), 973-1006
[12] Chen, G.; Dong, X., Identification and control of chaotic system: An artificial neural network approach, Proc. of the IEEE Int’l. Symp. on Circ. Sys., 3, 1177-1182 (1995), Seattle, WA
[13] Chen, G.; Chen, Y.; Ogmen, H., Identifying chaotic system via a Wiener-type cascade model, IEEE Contr. Sys. Magazine, 8, 29-36 (1997)
[14] Frison, T. W., Controlling chaos with a neural network, Proc. of Int’l. Conf. on Neural Networks, 75-80 (1992), Baltimore, MD
[15] Qin, H. S.; Zhang, H. Z.; Chen, G., Neural-network based adaptive control of uncertain chaotic system, Proc. of IEEE Int’l. Symp. on Circ. Sys., III, 318-321 (1998), Monterey, CA
[16] Cimagalli, V.; Jankowski, S.; Giona, M.; Calascibetta, T., Neural networks reconstruction and prediction of chaotic dynamics, Proc. of IEEE Int’l. Symp. on Circ. and Sys., 2176-2179 (1993), Chicago, IL
[17] Narenda, K. S.; Parthasarathy, K., Identification and control of dynamical system using neural networks, IEEE Trans. on Neural Networks, 1, 4-27 (1990)
[18] Dror, S.; Collins, D., Identification and control of nonlinear time-varying dynamical systems using artificial neural networks, World Congress on Neural Networks (1993), Portland, OR
[19] Greblicki, W., Nonparametric identification of Wiener systems by orthogonal series, IEEE Trans. on Automatic Control, 39, 2077-2086 (1994) · Zbl 0824.93068
[20] Hunter, I., Identification of nonlinear biological systems: Wiener and Hammerstein models, Biological Cybernetics, 55, 135-144 (1986) · Zbl 0611.92002
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