Nonlinear identification using prior knowledge of fixed points: A multiobjective approach

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 13, Issue 5, 2003, Pages 1229-1246

  Nepomuceno, Erivelton G ^a   Takahashi, Ricardo H C ^a   Amaral, Gleison F V ^a   Aguirre, Luis A ^a  

^a FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

Author keywords

Fixed points; Gray box identification; Multiobjective optimization

Indexed keywords

IDENTIFICATION (CONTROL SYSTEMS); MATHEMATICAL MODELS; OPTIMIZATION;

FIXED POINTS;

NONLINEAR SYSTEMS;

EID: 0043200949     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127403007187     Document Type: Article

References (26)

1. Aguirre, L. A. & Mendes, E. M. [1996] "Nonlinear polynomial models: Structure, term clusters and fixed points," Int. J. Bifurcation and Chaos 6, 279-294.
2. Aguirre, L. A., Rodrigues, G. & Mendes, E. [1997] "Nonlinear identification and cluster analysis of chaotic attractor from a real implementation fo Chua's circuit," Int. J. Bifurcation and Chaos 7, 1411-1423.
3. Aguirre, L. & Souza, A. [1998] "An algorithm for estimating fixed points of dynamical systems from time series," Int. J. Bifurcation and Chaos 8, 2203-2213.
4. Aguirre, L., Donoso-Garcia, P. & Santos-Filho, R. [2000] "Use of a priori information in the identification of global nonlinear model - a case study using a buck converter," IEEE Trans. Circuits Syst.-I 47, 1081-1085.
5. Aguirre, L. A., Letellier, C. & Maquet, J. [2002] "Induced one-parameter bifurcations in identified nonlinear models," Int. J. Bifurcation and Chaos 12, 135-145.
6. Billings, S. A., Chen, S. & Korenberg, M. J. [1989] "Identification of MIMO nonlinear systems using a forward-regression orthogonal estimator," Int. J. Contr. 49, 2157-2189.
7. Billings, S. A. & Coca, D. [1999] "Discrete wavelet models for identification and qualitative analysis of chaotic systems," Int. J. Bifurcation and Chaos 9, 1263-1284.
8. Broomhead, D. S. & Lowe, D. [1988] "Multivariable functional interpolation and adaptive networks," Compl. Syst. 2, 321-355.
9. Brown, R., Rulkov, N. & Tufillaro, N. [1994] "Nonlinear prediction of chaotic time series," Phys. Rev. E50, 4488-4508.
10. Casdagli, M., Eubank, S., Farmer, J. D. & Gibson, J. [1991] "State space reconstruction in the presence of noise," Physica D51, 52-98.
11. Chankong, V. & Haimes, Y. Y. [1983] Multiobjective Decision Making: Theory and Methodology (North-Holland-Elsevier, NY).
12. Chua, L. O. & Hasler, M. G. E. [1993] "Special issue on chaos in nonlinear electronic circuits," IEEE Trans. Circuits Syst.-I 40, 10-11.
13. Floriani, E., Dudok de Wit, T. & Le Gal, P. [2000] "Nonlinear interactions in a rotating disk flow: From a Volterra model to the Ginzburg-Landau equation," Chaos 10, 834-847.
14. Gibson, J. F., Farmer, J. D., Casdagli, M. & Eubank, S. [1992] "An analytic approach to practical state space reconstruction," Physica D57, p. 1.
15. 2 approximation on nets," Phys. Rev. E49, 4955-4972.
16. Irving, A. D. & Dewson, T. [1997] "Determining mixed linear-nonlinear coupled differential equations from multivariate discrete time series sequences," Physica D102, 15-36.
17. Johansen, T. [1996] "Identification of non-linear systems using empirical data and prior knowledge - an optimization approach," Automatica 32, 337-356.
18. Kugiumtzis, D. [1996] "State space reconstruction parameters in the analysis of chaotic time series - the role of time series length," Physica D95, 13-28.
19. Lainscsek, C. S. M., Schürrer, F. & Kadtke, J. [1998] "A general form for global dynamical data models for three-dimensional systems," Int. J. Bifurcation and Chaos 8, 899-914.
20. Leontaritis, I. J. & Billings, S. A. [1985] "Input-output parametric models for non-linear systems - Part II: Stochastic non-linear systems," Int. J. Contr. 41, 329-344.
21. Letellier, C., Maquet, J., Le Sceller, L. & Aguirre, L. A. [1998] "On the non-equivalence of observables in phase-space reconstructions from recorded time series," J. Phys. A31, 7913-7927.
22. Packard, N. H., Crutchfield, J. P., Farmer, J. D. & Shaw, R. S. [1980] "Geometry from a time series," Phys. Rev. Lett. 45, 712-716.
23. Rosenstein, M. T., Collins, J. J. & De Luca, C. J. [1994] "Reconstruction expansion as a geometry-based framework for choosing proper delay times," Physica D73, 82-98.
24. Sauer, T., Yorke, J. A. & Casdagli, M. [1991] "Embedology," J. Statist. Phys. 65, 579-616.
25. Suykens, J. A. K. & Vandewalle, J. [1995] "Learning a simple recurrent neural state space model to behave like Chua's double scroll," IEEE Trans. Circuits Syst.-I 42, 499-502.
26. Takens, F. [1981] "Detecting strange attractors in turbulence," Dynamical Systems and Turbulence, Lecture Notes in Mathematics, Vol. 898, eds. Rand, D. A. & Young, L. S. (Springer-Verlag, Berlin), pp. 366-381.