A weights-directly-determined simple neural network for nonlinear system identification

Based on polynomial interpolation and approximation theory, a special feed-forward neural network using power activation functions is constructed in this paper. The neural model employs a three-layer structure with the hidden-layer neurons activated by a group of order-increasing power functions (while other layerspsila neurons use linear activation functions). In addition, the weights-updating formula for such a neural network could be derived from the standard BP training method. A pseudoinverse-based method (or termed, weights-direct-determination/one-step-weights-determination method) is then established to determine immediately the neural-network weights without lengthy iterative BP-training. It is shown that such a power-activated feed-forward neural network could perform effectively and efficiently for nonlinear system identification. Computer-simulation results further substantiate the benefits of its weights-direct-determination method.