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Adaptive wavelet neural networks for nonlinear modelling and control. (English) Zbl 1162.68551

Summary: Feed-forward and recurrent neural networks have been successfully used for modelling and control of nonlinear 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 piecewise smooth functions, with rather sharp transitions between neighbouring domains. The combination of wavelet theory and neural networks has led to the development of Wavelet Neural 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 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 system. Simulation results demonstrate the applicability of the proposed design method to nonlinear control systems.

MSC:

68T05 Learning and adaptive systems in artificial intelligence
93C83 Control/observation systems involving computers (process control, etc.)
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