Nonlinear Complex Dynamical Systems Modeling and Adaptive Control Based on a Novel Diagonally Expanded Functional Link Neural Network (DEFLNN)

This paper proposes a novel approach for the identification and adaptive control of non-linear dynamical systems using a new neural network architecture called Diagonally Expanded Functional Link Neural Network (DEFLNN). The DEFLNN model is computationally efficient, with a simpler architecture that requires fewer adjustable parameters compared to traditional Recurrent Neural Networks (RNNs). This model uses Chebyshev polynomial function expansion and introduces a feedback loop that applies diagonal weights to the output. The performance of the DEFLNN is compared with other recurrent models, including Elman, Diagonal, and Jordan Recurrent Neural Networks, as well as standard Functional Link Neural Networks (FLNNs). The Back Propagation (BP) algorithm is used to update the weights of the DEFLNN model. Two distinct non-linear dynamical systems are employed to validate and assess the robustness of the proposed model through simulations over a fixed number of iterations. Next, a DEFLNN-based controller is designed whose structure is similar to that of the DEFLNN model but with a difference in input and output. The input of the controller is an error, while the output of the controller acts as a input to the plant. The output of the proposed controller is then evaluated with and without disturbances, and its performance is compared with other RNN controllers.