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Back-propagation with gradient method is the most popular learning algorithmfor feed-forward neural networks. However, it is critical to determine a properfixed learning rate for the algorithm. In this paper, an optimized recursivealgorithm is presented for online learning based on matrix operation andoptimization methods analytically, which can avoid the trouble to select aproper learning rate for the gradient method. The proof of weak convergence ofthe proposed algorithm also is given. Although this approach is proposed forthree-layer, feed-forward neural networks, it could be extended to multiplelayer feed-forward neural networks. The effectiveness of the proposedalgorithms applied to the identification of behavior of a two-input andtwo-output non-linear dynamic system is demonstrated by simulation experiments.

An Optimized Recursive Learning Algorithm for Three-Layer Feedforward Neural Networks For Mimo Nonlinear System Identifications