Multilayer feedforward networks are universal approximators
Neural Networks
Neural Computation
Neural Systems for Control
Wavelet differential neural network observer
IEEE Transactions on Neural Networks
Wavelet neural networks for function learning
IEEE Transactions on Signal Processing
Universal approximation bounds for superpositions of a sigmoidal function
IEEE Transactions on Information Theory
Using wavelet network in nonparametric estimation
IEEE Transactions on Neural Networks
Gradient methods for the optimization of dynamical systems containing neural networks
IEEE Transactions on Neural Networks
A new class of wavelet networks for nonlinear system identification
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Multidimensional wavelet frames
IEEE Transactions on Neural Networks
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In this paper, identification problem of a general class of nonlinear dynamic systems is fully considered using adaptive wavelet differential neural networks. In these networks, the activation functions are described by wavelets where parameters are tuned adaptively. The stability analysis of such identifiers is performed by means of Lyapunov analysis. Asymptotic convergence of the error and boundedness of the parameters are proven. To validate the approach, the neuro-identifier is applied to both the Van der pole oscillator and the twin-tanks plant. The simulation results show that the proposed neuro-identifier outperforms the sigmoid based differential neural network identifier.