Nonlinear black-box models in system identification: Mathematical foundations

Automatica

Volumn 31, Issue 12, 1995, Pages 1725-1750

  Juditsky, Anatoli ^a   Hjalmarsson, Håkan ^b   Benveniste, Albert ^a   Delyon, Bernard ^a   Ljung, Lennart ^b   SjÖberg, Jonas ^b   Zhang, Qinghua ^a  

^a CAMPUS DE BEAULIEU   (France)

^b LINKÖPING UNIVERSITY   (Sweden)

Author keywords

neural networks; Non parametric identification; nonlinear systems; wavelet estimators

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; ERRORS; MATHEMATICAL MODELS; NEURAL NETWORKS; NONLINEAR SYSTEMS; PARAMETER ESTIMATION; RANDOM PROCESSES; REGRESSION ANALYSIS; WAVELET TRANSFORMS;

MATHEMATICAL FOUNDATIONS; NONLINEAR BLACK BOX MODELS; SPATIALLY ADAPTIVE APPROXIMANT; STOCHASTIC ERROR; WAVELET ESTIMATOR;

IDENTIFICATION (CONTROL SYSTEMS);

EID: 0029482971     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/0005-1098(95)00119-1     Document Type: Article

References (68)

1. Statistical predictor identification
2. Universal approximation bounds for superpositions of a sigmoidal function
3. On a family of functional spaces: embedding theorems and applications
4. Hinging hyperplanes for regression, classification and function approximation
5. Smoothing noisy data with spline functions
6. Wavelet estimators, global error measures revisited
7. Optimal estimators for functional autoregression
8. Accuracy analysis for wavelet networks
9. Any discrimination rule can have an arbitrary bad probability of error for final sample size
10. Distribution free consistency result in nonparametric discrimination and regression function estimation
11. Projection-based approximation and a duality with kernel methods
12. Minimax estimation via wavelet shrinkage
13. p-balls
14. Adapting to unknown smoothness via wavelet shrinkage
15. Density estimation by wavelet thresholding
16. Wavelet shrinkage: asymptopia
17. Estimation of square-integrable spectral density based on a sequence of observations
18. Estimation of square-integrable probability density of a random variable
19. Variable bandwidth and local linear regression smoothers
20. Multivariate adaptive regression splines (with discussion)
21. Projection pursuit regression
22. Optimal bandwidth selection in nonparametric regression function estimation
23. Projection pursuit (with discussion)
24. Neural networks for control systems—a survey
25. Wavelets and PDE
26. Compression of wavelet decompositions
27. Adaptive wavelet estimators
28. Density estimation in Besov spaces
29. On the representation of continuous functions of several variables by superpositions of continuous functions of one variable and addition
30. l and generalized cross-validation in ridge regression and application to the spline smoothing
31. l and generalized cross-validation: discrete index set
32. The 13th problem of Hilbert
33. Statistical predictor identification
34. Problems in the analysis of survey data and a proposal
35. Variable bandwidth kernel estimators of regression curves
36. On estimating regression
37. Nonparametric estimation of smooth regression functions
38. t, tϵn
39. On estimation of probability density function and the mode
40. Networks for approximation and learning
41. p criterion for projection regression estimates
42. Estimation non paramétrique et commande adaptative de processus Markoviens non linéaires
43. Bandwidth choice for nonparametric regression
44. Remarks on some nonparametric estimates of density functions
45. Curve estimation
46. n
47. Nonlinear black-box modeling in system identification: a unified overview
48. Nonlinear regulation the piecewise linear approach
49. Optimal global rates of convergence for nonparametric regression
50. Nonparametric regression: optimal local bandwidth choice
51. Smooth regression analysis