localizability, lack of a systematic method for structure selection and slow convergence of approximation. To overcome the lack of localization and global approximation of neural networks, the global activation function is substituted with a localized and compact support function

In this paper, a wavelet-based neural network is proposed for the control of nonlinear systems. Activation functions of neural network nodes are determined based on the wavelet transform. The controller can efficiently compensate for the undesired effects of hard nonlinearities such as saturation and/or dead zone of control input. Compared with standard neuro-controllers, the structure of the controller is definite and simple. The proposed controller is localizable and has a systematically chosen structure, which improves the closeloop performance. An off-line algorithm determines the number of nodes. In addition, an on-line algorithm adjusts the parameters of wavelet bases and network weights. Back propagation algorithm with a momentum term is used for updating the weights and parameters of activation functions. This controller reduces the quantity of network parameters, calculation cost and convergence time of online algorithms with respect to the conventional neural network. Also, the controller is able to control unstable and MIMO systems. To illustrate the capability and performance superiority of the proposed controller, two nonlinear systems are controlled and the corresponding results are compared.