Ten lectures on wavelets
On characterizations of the input-to-state stability property
Systems & Control Letters
Robust adaptive control
Identification of nonlinear dynamical systems using multilayered neural networks
Automatica (Journal of IFAC)
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Information Sciences—Informatics and Computer Science: An International Journal - Special issue: Informatics and computer science intelligent systems applications
Discrete time recurrent neural network observer
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Wavelet neural networks for function learning
IEEE Transactions on Signal Processing
Using wavelet network in nonparametric estimation
IEEE Transactions on Neural Networks
Stable dynamic backpropagation learning in recurrent neural networks
IEEE Transactions on Neural Networks
Some new results on system identification with dynamic neural networks
IEEE Transactions on Neural Networks
Identification and control of dynamical systems using neural networks
IEEE Transactions on Neural Networks
A new class of wavelet networks for nonlinear system identification
IEEE Transactions on Neural Networks
Learning and convergence analysis of neural-type structured networks
IEEE Transactions on Neural Networks
Nonlinear Adaptive Wavelet Control Using Constructive Wavelet Networks
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
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Since wavelet transform uses the multi-scale (or multi-resolution) techniques for time series, wavelet transform is suitable for modeling complex signals. Haar wavelet transform is the most commonly used and the simplest one. The Haar wavelet neural network (HWNN) applies the Harr wavelet transform as active functions. It is easy for HWNN to model a nonlinear system at multiple time scales and sudden transitions. In this paper, two types of HWNN, feedforward and recurrent wavelet neural networks, are used to model discrete-time nonlinear systems, which are in the forms of the NARMAX model and state-space model. We first propose an optimal method to determine the structure of HWNN. Then two stable learning algorithms are given for the shifting and broadening coefficients of the wavelet functions. The stability of the identification procedures is proven.