Regularization techniques for identification using local-affine models;Regularisierungsverfahren für die Identifikation mittels lokal-affiner Modelle

At-Automatisierungstechnik

Volumn 56, Issue 7, 2008, Pages 339-349

  Zimmerschied, Ralf ^a   Isermann, Rolf ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Global local regularization; Global local parameter estimation; Local affine models; Nonlinear equation output error; Nonlinear identification; Tikhonov regularization

Indexed keywords

EID: 62549119973     PISSN: 01782312     EISSN: None     Source Type: Journal    
DOI: 10.1524/auto.2008.0717     Document Type: Article

References (20)

1. Bishop, Christopher M.: "Neural Networks for Pattern Recognition", Oxford University Press 1995.
2. Bossley, Kevin M.: "Neurofuzzy Modelling Approaches in System Identification", Doktorarbeit, University of Southampton 1997.
3. Cao, Shu G.; Rees, Neville W.; Feng, Gang: "Analysis and Design for a Class of Complex Control Systems, Part I: Fuzzy Modelling and Identification", In: Automatica 33 (1997) Nr. 6, S. 1017-1028.
4. Chen, Zhe; Haykin, Simon: "On Different Facets of Regularization Theory", In: Neural Computation 14 (2002), S. 2791-2846.
5. Geman, Stuart; Bienenstock, Elie; Doursat, René: "Neural Networks and the Bias/Variance Dilemma", In: Neural Computation 4 (1992), S. 1-58.
6. Golub, Gene H.; Van Loan, Charles F.: "Matrix Computations", The John Hopkins University Press 1996.
7. Hansen, Per C.: "Analysis of Discrete Ill-Posed Problems by Means of the L-Curve", In: SIAM Review 34 (1992) Nr. 4, S. 561-580.
8. Hoerl, Arthur E.; Kennard, Robert W.: "Ridge Regression: Biased Estimation for Nonorthogonal Problems", In: Technometrics 12 (1970) Nr. 1, S. 55-67.
9. Isermann, Rolf; Ernst, Susanne; Nelles, Oliver: "Identification with dynamic neural networks - Architectures, comparisions, applications", Plenary in: Proc. IFAC Symposium on System Identification 1997, Fukuoka, Japan, S. 997-1022.
10. Isermann, Rolf: "Identifikation dynamischer Systeme, Band 1 und 2", Springer-Verlag, Berlin 1992.
11. Johansen, Tor A.: "On Tikhonov regularization, bias and variance in nonlinear system identification", In: Automatica 33 (1997) Nr. 3, S. 441-446.
12. Johansen, Tor A.: "Robust identification of Takagi-Sugeno-Kang fuzzy models using regularization", In: Proc. IEEE Conf. Fuzzy Systems 1996, New Orleans, S. 180-186.
13. Johansen, Tor A.; Babuška, Robert: "Multiobjective Identification of Takagi-Sugeno Fuzzy Models", In: IEEE Transaction on Fuzzy Systems 11 (2003) Nr. 6, S. 847-860.
14. Moody, J. E.: "The Effective Number of Parameters: An Analysis of Generalization and Regularization in Nonlinear Learning Systems", In: Advances in Neural Information Processing Systems 4, S. 847-854, Morgan Kaufmann Publishers, San Mateo 1992.
15. Moré, Jorge J.: "The Levenberg-Marquardt Algorithm: Implementation and Theory", In: Lecture Notes in Mathematics: Numerical Analysis, S. 105-116, Springer-Verlag 1978.
16. Murray-Smith, Roderick; Johansen, Tor A.: "Local Learning in Local Model Networks", In: Multiple Model Approaches to Modelling and Control, S. 185-210, Taylor & Francis Ltd., London 1997.
17. Nelles, O.: "Nonlinear System Identification", Springer-Verlag, Berlin 2001.
18. Tikhonov, Andrey N.; Arsenin, Vasiliy Y.: "Solutions of illposed problems", John Wiley & Sons 1977.
19. Töpfer, Susanne: "Hierarchische neuronale Modelle für die Identifikation nichtlinearer Systeme", VDI Verlag GmbH, Düsseldorf 2002.
20. Yen, John; Wang, Liang; Gillespie, Charles W.: "Improving the Interpretability of TSK Fuzzy Models by Combining Global Learning and Local Learning", In: IEEE Transaction on Fuzzy Systems 6 (1998) Nr. 4, S. 530-537.