A stable framework-based modeling of the complex dynamical system using a double context layered with self-weighted output feedback loop Elman recurrent neural network

Abstract

In this paper, a modified structure of the classical Elman recurrent neural network (ERNN) named Double context layered with output self-weighted feedback loop Elman recurrent neural network (DCLOSWFLERNN) is proposed. It consists of two additional components (as compared to the ERNN model): one extra context layer and an adjustable weighted feedback loop in the output layer. This has resulted in the model's ability to approximate the underlying unknown mathematical relationship relating to the input-output data (obtained from any complex dynamical plant). The second emphasis of this paper pertains to the stability component, wherein the Lyapunov stability is utilized to develop a stable Back-propagation (BP) based weight update rule. Lastly, an adjustable learning rate is also suggested, which contributes to improving the learning algorithm's overall performance. The simulation results reveal that the proposed model has given better modeling accuracy as compared to the other considered neural models. This can be observed from the values obtained of the error-based indicators such as Root Mean Square Error (RMSE) and Mean Average Error (MSE). The values of RMSE and MAE obtained from the proposed model during the modeling procedure are 0.0028 and 0.0035 which are the least among the obtained with other neural models.