Improved Pi-Sigma Neural Network for nonlinear system identification

In this paper, we propose a modified architecture of a Pi-Sigma Neural Network (PSNN) based on two modifications: extension of the activation function and adding delays to neurons in the hidden layer. These new networks are called respectively Activation Function Extended Pi-Sigma (AFEPS) and Delayed Pi-Sigma (DPS) are obtained first by adding an activation function to all hidden neurons and secondly by modifying the PSNN so its hidden layer outputs are fed to temporal adjustable units that permit to this new network to be capable to identify nonlinear systems. Architecture and dynamic equations of these networks are given in details with their training algorithm. To ensure the effectiveness of our proposed networks, examples of nonlinear system identification are provided. The obtained results show the capacity of HONNs for the nonlinear systems identification. In particular, the proposed neural architectures (AFEPS and DPS) provide better results due to the modifications made on them.