Nonlinear dynamic engineering processes modeling using a lyapunov-stability based novel locally connected recurrent pi-sigma neural network: design, simulation, and a comparative study

In this paper, a recurrent version of the classical Pi-Sigma Neural Network (PSNN) is proposed to model the unknown dynamics of nonlinear engineering processes. The proposed model called a Locally Connected Recurrent Pi-Sigma Neural Network (LCRPSNN), involves the weighted self-feedback connections associated with each of its hidden layer's neurons. These connections are valuable in inducing the memory property into the model which is responsible for improving its ability to approximate any unknown nonlinear dynamics. The proposed model is provided with the information of only two input signals: the present value of the external input and the unit-delayed output of the process output. This eliminates the need to know the order of the plant (which is generally used to select the number of inputs to the neural model) which, in most cases, is generally not known. To reduce the complexity of the model's structure only 3 hidden neurons are considered. The gradient-descent-based Back-Propagation (BP) learning algorithm is used to develop the recursive parameter update equations for the proposed model that are used to tune its parameter values. To accelerate the training process and to ensure the stability of the overall system an adaptive learning rate scheme is developed based on the principles of Lyapunov-stability theory. A total of three benchmark processes are used in the conducted simulation experiments on which the proposed model is applied and tested. To compare its performance with other well-known neural models we have considered the Elman Recurrent Neural Network (ERNN), Jordan Recurrent Neural Network (JRNN), Diagonal Recurrent Neural Network (DRNN), PSNN, and the Feed-Forward Neural Network (FFNN). The simulation results indicate that the proposed model has given better accuracy as compared to the other considered neural models.