Home > System Identification > 14th IFAC Symposium on System Identification, 2006 > Some aspects on nonlinear system identification
Some aspects on nonlinear system identification
System Identification, Volume # 14 | Part# 1
Location: , Australia
National Organizing Committee Chair: Brett Ninness,
Håkan Hjalmarsson
International Program Committee Chair: Iven Mareels
Conference Editor: Brett Ninness,
Håkan Hjalmarsson
Authors
Lennart Ljung
Identifier
10.3182/20060329-3-AU-2901.00085
Index Terms
nonlinear system identification,neural networks,nonlinear models
Abstract
Identification of nonlinear systems is a very extensive problem, with roots and branches in several diverse fields. It is not possible to survey the area in a short text. The current presentation gives a subjective view on some essential features in the area. These concern a classification of methods, the use of different shades of grey in models, and some overall issues like bias-variance trade-offs, data sparseness and the peril of local minima.
References
[1] Andrieu, C., A. Doucet, S. S. Singh and V. B.
Tadić (2004). Particle methods for change
detection, system identification and control.
Proceeding of IEEE 92(3), 423-438.
[2] Bai, E. W. (2002). A blind approach to the
Hammerstein-Wiener model identification.
Automatica 38(6), 967-979.
[3] Bamieh, B. and L. Giarré (2002). Identification of
linear parameter varying models. Int. Journal
of Robust and Nonlinear Control 12, 841-853.
[4] Bartlett, P. L. (2003). Prediction algorithms:
complexity, concentration and convexity. In:
Proc. IFAC Symposium on Identification,
SYSID'03. Rotterdam, The Netherlands.
[5] Bemporad, A., A. Garulli, S. Paoletti and A. Vicino
(2003). A greedy approach to identification
of piecewise affine models. In: Hybrid
Systems, Computation and Control (O. Maler
and A. Pnueli, Eds.), pp. 97-112. Number
2623 In: Lecture Notes in Computer Science.
Springer Verlag.
[6] Billings, S. A. (1990). Identification of nonlinear
systems - a survey. IEE Proc. D 127, 272-
285.
[7] Boyd, S. and L. O. Shua (1985). Fading memory
and the problem of approximating non-linear
operators with volterra series. IEEE
Transactions on Circuits and Systems CAS-
32(11), 1150-1161.
[8] Enqvist, M. (2005). Linear Models of Nonlinear
Systems. PhD thesis. Linköping University,
Sweden. Linköping Studies in Science and
Technology. Dissertation No. 985.
[9] Fan, J. and I. Gijbels (1996). Local Polynomial
Modelling and Its Applications. number 66 In:
Monographs on Statistics and Applied Probability
. Chapman & Hall.
[10] Fukunaga, K. (1990). Introduction to statistical
pattern recognition (2nd ed.). Academic
Press, New York.
[11] Golub, G. H., M. Heath and G. Wahba (1979).
Generalized cross-validation as a method for
choosing a good ridge parameter. Technometrics
21(2), 215-223.
[12] Harris, C., X. Hong and Q. Gan (2002). Adaptive
Modelling, Estimation and Fusion from Data:
A Neurofuzzy Approach. Springer. New York.
[13] Hastie, T., R. Tibshirani and J. Friedman
(2001). The Elements of Statistical Learning.
Springer.
[14] Härdle, W. (1990). Applied Nonparametric Regression
. Cambridge Univeristy Press. Cambridge,
UK.
[15] Hsu, K., T. Vincent and K. Poolla (2006). A
kernel based approach to structured nonlinear
system identification part I: Algorithms, part
II: Convergence and consistency. In: Proc.
IFAC Symposium on System Identification.
Newcastle, Australia.
[16] Jang, J.-S. R. and C.-T. Sun (1995). Neuro-fuzzy
modeling and control. Proc. of the IEEE
83(3), 378-406.
[17] Johansen, T. A. and B. A. Foss (1995). Identification
of nonlinear-system structure and parameters
using regime decomposition. Automatica
31(2), 321-326.
[18] Lee, L. and K. Poolla (1999). Identification of
linear parameter-varying systems using non-linear
programming. ASME Journal of Dynamic
Systems, Measurement and Control
121, 71-78.
[19] Ljung, L. (1999). System Identification - Theory
for the User. 2nd ed., Prentice-Hall. Upper
Saddle River, N.J.
[20] Ljung, L. and T. Glad (1994). On global identifiability
of arbitrary model parameterizations.
Automatica 30(2), pp. 265-276.
[21] Magritte, R. (1929). Ceci n'est pas une pipe. In:
Los Angeles County Museum of Art.
[22] Milanese, M. and C. Novara (2005). Model quality
in identification of nonlinear systems.
IEEE Transactions on Automatic Control
AC-50(10), 1606-1611.
[23] Murray-Smith, R. and Johansen, T. A., (Eds.)
(1997). Multiple Model Approaches to Modeling
and Control. Taylor and Francis. London.
[24] Nadaraya, E. (1964). On estimating regression.
Theory of Prob. and Applic. 9, 141-142.
[25] Nelles, O. (2001). Nonlinear System Identification:
From Classical Approaches to Neural
Networks and Fuzzy Models. Springer Verlag.
Berlin.
[26] Roll, J., A. Bemporad and L. Ljung (2004). Identification
of piecewise affine systems via mixed-integer
programming. Automatica 40(1), 37-
50.
[27] Roll, J., A. Nazin and L. Ljung (2005). Non-linear
system identification via direct weight
optimization. Automatica 41(3), 475-490.
[28] Sacks, J. and D. Ylvisaker (1978). Linear estimation
for approximately linear models. The Annals
of Statistics 6(5), 1122-1137.
[29] Schittkowski, K. (2002). Numerical Data Fitting
in Dynamical Systems. Kluwer Academic
Publishers. Dordrecht.
[30] Schön, T. B., A. Wills and B. Ninness (2006).
Maximum likelihood nonlinear system estimation.
In: Proceedings of the 14th IFAC
Symposium on System Identification. Newcastle,
Australia. Accepted for publication.
[31] Schoukens, J., J. Nemeth, P. Crama, Y. Rolain
and R. Pintelon (2003). Fast approximate
identification of nonlinear systems. In: Proc.
13th IFAC Symposium on System Identification
(P. van der Hof, B. Wahlberg and
S. Weiland, Eds.), Rotterdam, The Netherlands.
pp. 61-66.
[32] Sjöberg, J., Q. Zhang, L. Ljung, A. Benveniste,
B. Delyon, P. Y. Glorennec, H. Hjalmarsson
and A. Juditsky (1995). Nonlinear black-box
modeling in system identification: A unified
overview. Automatica 31(12), 1691-1724.
[33] Suykens, J. A. K., T. van Gestel, J. De Brabanter,
B. De Moor and J. Vandewalle (2002). Least
Squares Support Vector Machines. World Scientific.
Singapore.
[34] Vapnik, V. (1998). Statistical Learning Theory.
Wiley.
[35] Zhang, Q. and A. Benveniste (1992). Wavelet networks.
IEEE Trans. Neural Networks 3, 889-
898.
