Hybrid training of RBF networks with application to nonlinear systems identification

The feedforward neural networks, including multiple layer perceptron (MLP) and radial basis function network (RBFN), are the most widely used networks due to their rapid training, generality, and simplicity. For RBFN, a traditional training algorithm consists of two stages: first learning in the hidden layer, which is typically performed using an unsupervised method such as a clustering algorithm; this is followed by a supervised learning in the output layer, such as recursive least squares (RLS) algorithms. Such a training algorithm has several drawbacks, including improper selection of RBF centers and over-size problem of the network in the first stage and ill-condition in the second. This paper proposes a new clustering algorithm based on constructing an augmented vector consisting of both input and output, and for training the RBFN using a U-D factorization based RLS algorithm which is superior to the standard RLS algorithm in convergence rate, numerical stability and accuracy of the training. The performance between RBFN and MLP with a sigmoidal function is also compared via simulation examples