Hierarchical Algorithms of Quasi-Linear ARX Neural Networks for Identification of Nonlinear Systems

A quasi-linear ARX neural network model (QARXNN) is a nonlinear model built using neural networks (NN). It has a linear-ARX structure where NN is an embedded system to give the parameters for the regression vector. There are two contributions in this paper, 1) Hierarchical Algorithms is proposed for the training of QARXNN model, 2) an adaptive learning is implemented to update learning rate in NN training to ensure global minima. First, the system is estimated by using LSE algorithm. Second, nonlinear sub-model performed using NN is trained to refine error of LSE algorithm. The linear parameters obtained from LSE algorithm is set as bias vector for the output nodes of NN. Global minima point is reached by adjusting the learning rate based on Lyapunov stability theory to ensure convergence of error. The proposed algorithm is used for the identification and prediction of nonlinear dynamic systems. Finally, the experiments and numerical simulations reveal that the proposed method gives satisfactory results.