Dynamic system identification based on a novel pi-sigma neural network with Lyapunov stability analysis

This research presents a novel recurrent model of the Pi-Sigma Neural Network (PSNN) named the Diagonally Layered Pi-Sigma Neural Network (DLPSNN) for identifying non-linear dynamical systems. The proposed model is an adaptation of PSNN with two additional layers, namely a feedback layer from the context to the hidden layer, and feedback from the unit time delay of the output to the tanh function. Pi-Sigma model contains both summation and multiplier units which improves the network's ability to model non-linear and complex relationships. The Back Propagation (BP) algorithm has been implemented to update the weights of various layers. The stability of the DLPSNN model is evaluated using Lyapunov-Stability (LS) principles. The DLPSNN model is tested on three non-linear dynamical systems and compared to other Neural Network (NN) models, such as classical PSNN, Feed-forward Neural Network (FNN), Elman Neural Network (ENN), Diagonal Neural Network (DNN), and Jordan Neural Network (JNN). It can be observed that the proposed model outperformed other NN models in terms of output accuracy and error minimization. The robustness of DLPSNN is tested under perturbation conditions, demonstrating its effective recovery capabilities from disturbances.