Rational wavelets in Wiener-like modeling

We use a Wiener-like approximation scheme using rational wavelets for the linear dynamical structure and a feedforward neural network for approximating the nonlinear static part. This class of structure allows us to approximate nonlinear oscillatory dynamic systems and has two main advantages: the time location of the dynamical components of the systems and the inclusion of the a priori knowledge of those components in the model.

[1]  Osvaldo Agamennoni,et al.  Approximate models for nonlinear dynamical systems and their generalization properties , 2001 .

[2]  M. Korenberg.  Statistical Identification of Parallel Cascades of Linear and Nonlinear Systems , 1982 .

[3]  Jonathan R. Partington,et al.  A Construction of Rational Wavelets and Frames in Hardy--Sobolev Spaces With Applications to System Modeling , 1998 .

[4]  M. Korenberg,et al.  Orthogonal approaches to time-series analysis and system identification , 1991, IEEE Signal Processing Magazine.

[5]  Yagyensh C. Pati.  Wavelets and Time-Frequency Methods in Linear Systems and Neural Networks , 1992 .

[6]  J. Dieudonne.  Foundations of Modern Analysis , 1969 .

[7]  Y. C. Pati,et al.  Rational wavelets in model reduction and system identification , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[8]  M. Schetzen.  The Volterra and Wiener Theories of Nonlinear Systems , 1980 .

[9]  Truong Q. Nguyen,et al.  Wavelets and filter banks , 1996 .

[10]  T. Poggio,et al.  The Volterra Representation and the Wiener Expansion: Validity and Pitfalls , 1977 .

[11]  Stephen A. Billings,et al.  Identi cation of nonlinear systems-A survey , 1980 .

[12]  Alfredo C. Desages,et al.  Wiener modelling using canonical pieciewise linear functions , 1999 .

[13]  R. Duffin,et al.  A class of nonharmonic Fourier series , 1952 .

[14]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[15]  Ingrid Daubechies,et al.  The wavelet transform, time-frequency localization and signal analysis , 1990, IEEE Trans. Inf. Theory.

[16]  John N. Tsitsiklis,et al.  Worst-Case Identification of Nonlinear Fading Memory Systems , 1992, 1992 American Control Conference.

[17]  Albert Nigrin,et al.  Neural networks for pattern recognition , 1993 .

[18]  K. Hoffman.  Banach Spaces of Analytic Functions , 1962 .

[19]  Alfredo C. Desages,et al.  Approximate models for nonlinear process control , 1996 .

[20]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[21]  Gerald Kaiser,et al.  A Friendly Guide to Wavelets , 1994 .

[22]  P. Duren.  Theory of Hp Spaces , 2000 .

[23]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[24]  M. B. Matthews,et al.  The identification of nonlinear discrete-time fading-memory systems using neural network models , 1994 .

[25]  C. Chui.  Wavelet Analysis and Its Applications , 1992 .

[26]  Leon O. Chua,et al.  Fading memory and the problem of approximating nonlinear operators with volterra series , 1985 .

[27]  Rui J. P. de Figueiredo,et al.  Nonlinear Feedback Control Systems: An Operator Theory Approach , 1993 .

[28]  Stephen A. Billings,et al.  Properties of neural networks with applications to modelling non-linear dynamical systems , 1992 .

[29]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[30]  S. Mallat.  A wavelet tour of signal processing , 1998 .