Training wavelet networks for nonlinear dynamic input-output modeling

Abstract In the framework of nonlinear process modeling, we propose training algorithms for feedback wavelet networks used as nonlinear dynamic models. An original initialization procedure is presented that takes the locality of the wavelet functions into account. Results obtained for the modeling of several processes are presented; a comparison with networks of neurons with sigmoidal functions is performed.

[1]  G. MallatS. A Theory for Multiresolution Signal Decomposition , 1989 .

[2]  A. U. Levin,et al.  Neural networks in dynamical systems: a system theoretic approach , 1992 .

[3]  Yagyensh C. Pati,et al.  Analysis and synthesis of feedforward neural networks using discrete affine wavelet transformations , 1993, IEEE Trans. Neural Networks.

[4]  Richard D. Braatz,et al.  On the "Identification and control of dynamical systems using neural networks" , 1997, IEEE Trans. Neural Networks.

[5]  Pierre Roussel-Ragot,et al.  Neural Networks and Nonlinear Adaptive Filtering: Unifying Concepts and New Algorithms , 1993, Neural Computation.

[6]  Léon Personnaz,et al.  BLACK-BOX MODELING WITH STATE-SPACE NEURAL NETWORKS , 1995 .

[7]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..

[8]  Kurt Hornik,et al.  Degree of Approximation Results for Feedforward Networks Approximating Unknown Mappings and Their Derivatives , 1994, Neural Computation.

[9]  L. Personnaz,et al.  The selection of neural models of nonlinear dynamical systems by statistical tests , 1994, Proceedings of IEEE Workshop on Neural Networks for Signal Processing.

[10]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Jun Zhang,et al.  Wavelet neural networks for function learning , 1995, IEEE Trans. Signal Process..

[12]  Kumpati S. Narendra,et al.  Neural Networks In Dynamical Systems , 1990, Other Conferences.

[13]  P. Pucar,et al.  Smooth Hinging Hyperplanes - An Alternative to Neural Nets , 1995 .

[14]  Pierre Roussel-Ragot,et al.  Training recurrent neural networks: why and how? An illustration in dynamical process modeling , 1994, IEEE Trans. Neural Networks.

[15]  Jean-Jacques E. Slotine,et al.  Space-frequency localized basis function networks for nonlinear system estimation and control , 1995, Neurocomputing.

[16]  E. Polak,et al.  Computational methods in optimization : a unified approach , 1972 .