Identification of non-linear systems using empirical data and prior knowledge - An optimization approach

Automatica

Volumn 32, Issue 3, 1996, Pages 337-356

  Johansen, Tor A ^a,b  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

^b SINTEF   (Norway)

Author keywords

Non linear systems; Optimization; Regularization; System identification

Indexed keywords

IDENTIFICATION (CONTROL SYSTEMS); MATHEMATICAL MODELS; OPTIMIZATION;

PENALTY TERMS; PRIOR KNOWLEDGE;

NONLINEAR SYSTEMS;

EID: 0030109138     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/0005-1098(95)00146-8     Document Type: Article

References (38)

1. Adams, R. A. (1975). Sobolev Spaces. Academic Press, New York.
2. Akaike, H. (1969). Fitting autoregressive models for prediction. Ann. Inst. Stat. Math., 21, 243-247.
3. Bishop, C. (1991). Improving the generalization properties of radial basis function neural networks. Neural Computation, 3, 579-588.
4. Breiman, L. (1993). Hinging hyperplanes for regression, classification, and function approximation. IEEE Trans. Information Theory, 39, 999-1013.
5. Demuth, H. and M. Beale (1993). Neural Network Toolbox User's Guide (MATLAB). The MathWorks, Inc.
6. Dyn, N. (1989). Interpolation and approximation by radial and related functions. In Approximation Theory IV(C. K. Chui, L. L. Schumaker and J. D. Ward, Eds), Vol. 1. pp. 211-234. Academic Press, New York.
7. Gill, P. E., W. Murray and M. H. Wright (1981). Practical Optimization. Academic Press, New York.
8. Girosi, F., M. Jones and T. Poggio (1994). Priors, stabilizers and basis functions: From regularization to radial, tensor and additive splines. Technical Report AI Memo 1430. MIT, Cambridge, MA.
9. Girosi, F., M. Jones and T. Poggio (1995). Regularization theory and neural network architectures. Neural Computation, 7, 219-269.
10. Grace, A. (1990). Optimization Toolbox User's Guide (MATLAB). The MathWorks, Inc.
11. Gustafsson, T. K. and K. V. Waller (1983). Dynamic modeling and reaction invariant control of pH. Chemical Engineering Science, 38, 389-398.
12. Hall, R. C. and D. E. Seborg (1989). Modelling and self-tuning control of a multivariable pH neutralization process. Part I: Modelling and multiloop control. In Proceedings of the American Control Conference, Pittsburgh, Vol. 2. pp. 1822-1827.
13. Joerding, W. H. and J. L. Meador (1991). Encoding a prior information in feedforward networks. Neural Networks, 4, 847.
14. Johansen, T. A. and B. A. Foss (1992). Representing and learning unmodeled dynamics with neural network memories. In Proceedings of the American Control Conference, Chicago, IL, pp. 3037-3043.
15. Johansen, T. A. and E. Weyer (1995). Model structure identification using separate validation data - asymptotic properties. In Proceedings of the European Control Conference, Rome, pp. 833-838.
16. Kramer, M. A., M. L. Thompson and P. M. Phagat (1992). Embedding theoretical models in neural networks. In Proceedings of the American Control Conference, Chicago, IL, pp. 475-479.
17. Larsen, J. and L. K. Hansen (1994). Generalization performance of regularized neural network models. In Proc. IEEE Workshop on Neural Networks for Signal Processing, Ermioni, Greece.
18. Leontaritis, I. J. and S. A. Billings (1985). Input-output parametric models for non-linear systems. Int. J. Control, 41, 303-344.
19. Luenberger, D. G. (1969). Optimization by Vector Space Methods. John Wiley, New York.
20. Luenberger, D. G. (1984). Introduction to Linear and Nonlinear Programming, 2nd Edn. Addison-Wesley, Reading, MA.
21. MacKay, D. J. C. (1991). Bayesian Methods for Adaptive Models. PhD thesis. California Institute of Technology, Pasadena, CA.
22. Madych, W. R. and S. A. Nelson (1990). Multivariate interpolation and conditionally positive definite functions. II. Mathematics of Computation, 54, 211-230.
23. Mosca, E. (1970). System identification by reproducing kernel hilbert space methods. In Preprints 2nd IFAC Symposium on Identification and Process Parameter Estimation, Prague. Paper 1.1.
24. O'Sullivan, F. (1986). A statistical perspective on ill-posed inverse problems. Statistical Science, 1, 502-527.
25. Sjöberg, J. and L. Ljung (1992a). A comment of "leakage" in adaptive algorithms. In Preprints IFAC Symposium on Adaptive Systems in Control and Signal Processing, Grenoble, France.
26. Sjöberg, J. and L. Ljung (1992b). Overtraining, regularization, and searching for minimum in neural networks. In Preprints IFAC Symposium on Adaptive Systems in Control and Signal Processing, Grenoble, France, pp. 669-674.
27. Sjöberg, J., T. McKelvey and L. Ljung (1993). On the use of regularization in system identification. In Preprints 12th IFAC World Congress, Sydney, Vol. 7. pp. 381-386.
28. Söderström, T. and P. Stoica (1988). System Identification. Prentice Hall, Englewood Cliffs, NJ.
29. Stoica, P., P. Eykhoff, P. Janssen and T. Söderström (1986). Model-structure selection by cross-validation. Int. J. Control, 43, 1841-1878.
30. Su, H.-T., N. Bhat and T. J. McAvoy (1992). Integrated neural networks with first principles models for dynamic modeling. In Preprints IFAC DYCORD+ '92, College Park, MD.
31. Suykens, J. A. K., B. L. R. De Moor and J. Vandewalle (1994). Static and dynamic stabilizing neural controllers, applicable to transition between equilibrium points. Neural Networks, 7, 819-831.
32. Tanaka, Y., M. Fukushima and T. Ibaraki (1988). A comparative study of several semi-infinite nonlinear programming algorithms. European Journal of Operational Research, 36, 92-100.
33. Thompson, M. L. and M. A. Kramer (1994). Modeling chemical processes using prior knowledge and neural networks. AIChE J., 40, 1328-1340.
34. Tikhonov, A. N. and V. Y. Arsenin (1977). Solutions of Ill-posed Problems. Winston, Washington DC.
35. Tulleken, H. J. A. F. (1993). Grey-box modelling and identification using physical knowledge and bayesian techniques. Automatica, 29, 285-308.
36. Wahba, G. (1990). Spline Models for Observational Data. SIAM, Philadelphia.
37. Weigend, A. S., B. A. Huberman and D. E. Rumelhart (1990). Predicting the future: a connectionist approach. International Journal of Neural Systems, 1, 193-209.
38. Williams, P. M. (1995). Bayesian regularization and pruning using a Laplace operator. Neural Computation, 7, 117-143.