A self-tuning fuzzy controller
Fuzzy Sets and Systems
An introduction to wavelets
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Adaptive fuzzy systems and control: design and stability analysis
Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence
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On the solution of differential equations with fuzzy spline wavelets
Fuzzy Sets and Systems
Foundations of Wavelet Networks and Applications
Foundations of Wavelet Networks and Applications
Adaptive modelling, estimation and fusion from data: a neurofuzzy approach
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Applied Soft Computing
Direct adaptive self-structuring fuzzy controller for nonaffine nonlinear system
Fuzzy Sets and Systems
Wavelet neural networks for function learning
IEEE Transactions on Signal Processing
Prediction and identification using wavelet-based recurrent fuzzy neural networks
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Fuzzy wavelet networks for function learning
IEEE Transactions on Fuzzy Systems
Reinforcement Hybrid Evolutionary Learning for Recurrent Wavelet-Based Neurofuzzy Systems
IEEE Transactions on Fuzzy Systems
Two-Mode Adaptive Fuzzy Control With Approximation Error Estimator
IEEE Transactions on Fuzzy Systems
Stable adaptive fuzzy control of nonlinear systems
IEEE Transactions on Fuzzy Systems
The wavelet transform, time-frequency localization and signal analysis
IEEE Transactions on Information Theory
Using wavelet network in nonparametric estimation
IEEE Transactions on Neural Networks
Unification of neural and wavelet networks and fuzzy systems
IEEE Transactions on Neural Networks
Bayesian wavelet networks for nonparametric regression
IEEE Transactions on Neural Networks
Orthogonal least squares learning algorithm for radial basis function 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
Analysis and synthesis of feedforward neural networks using discrete affine wavelet transformations
IEEE Transactions on Neural Networks
Multidimensional wavelet frames
IEEE Transactions on Neural Networks
Fuzzy wavelet neural network models for prediction and identification of dynamical systems
IEEE Transactions on Neural Networks
Adaptive fuzzy wavelet neural controller design for chaos synchronization
Expert Systems with Applications: An International Journal
A hierarchical structure of observer-based adaptive fuzzy-neural controller for MIMO systems
Fuzzy Sets and Systems
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This paper presents a new adaptive fuzzy wavelet network controller (A-FWNC) for control of nonlinear affine systems, inspired by the theory of multiresolution analysis (MRA) of wavelet transforms and fuzzy concepts. The proposed adaptive gain controller, which results from the direct adaptive approach, has the ability to tune the adaptation parameter in the THEN-part of each fuzzy rule during real-time operation. Each fuzzy rule corresponds to a sub-wavelet neural network (sub-WNN) and one adaptation parameter. Each sub-WNN consists of wavelets with a specified dilation value. The degree of contribution of each sub-WNN can be controlled flexibly. Orthogonal least square (OLS) method is used to determine the number of fuzzy rules and to purify the wavelets for each sub-WNN. Since the efficient procedure of selecting wavelets used in the OLS method is not very sensitive to the input dimension, the dimension of the approximated function does not cause the bottleneck for constructing FWN. FWN is constructed based on the training data set of the nominal system and the constructed fuzzy rules can be adjusted by learning the translation parameters of the selected wavelets and also determining the shape of membership functions. Then, the constructed adaptive FWN controller is employed, such that the feedback linearization control input can be best approximated and the closed-loop stability is guaranteed. The performance of the proposed A-FWNC is illustrated by applying a second-order nonlinear inverted pendulum system and compared with previously published methods. Simulation results indicate the remarkable capabilities of the proposed control algorithm. It is worth noting that the proposed controller significantly improves the transient response characteristics and the number of fuzzy rules and on-line adjustable parameters are reduced.