Adaptive wavelet neural networks for non-linear modelling and control

Feed-forward and recurrent neural networks have been successfully used for modelling and control of non-linear systems. The main features of these systems such as the ability to learn from examples and to self-adapt are very well suited for the multi-resolution approach intrinsic to wavelets. Wavelets offer an adequate framework for the representation of "natural" signals and images that are described by piece-wise smooth functions, with rather sharp transitions between neighbouring domains. The combination of wavelet theory and neural networks has lead to the development of wavelet networks (WNNs). WNNs are neural networks using wavelets as activation function, where both the position and the dilation of the wavelets are optimised besides the weights. Their strength lies in the capability of catching essential features in "frequency-rich" signals. In this paper an infinite impulse response (IIR) recurrent structure is combined in cascade to a WNN in a proposed controller-scheme. The effectiveness of the proposed controller is illustrated through an application to composition control in a continuously stirred tank reactor (CSTR) system. Simulation results demonstrate the applicability of the proposed design method to non-linear control systems. © Dynamic Publishers, Inc.