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Local Recurrent Sigma Pi Artificial Neural Network‐Based Adaptive Control of Nonlinear Dynamical Systems.

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Bibliographic Details
Title:	Local Recurrent Sigma Pi Artificial Neural Network‐Based Adaptive Control of Nonlinear Dynamical Systems.
Authors:	Saini, Kartik¹ (AUTHOR) kartiksaini17@gmail.com, Kumar, Narendra¹ (AUTHOR), Bhushan, Bharat¹ (AUTHOR), Kumar, Rajesh² (AUTHOR)
Source:	Optimal Control - Applications & Methods. Mar2026, Vol. 47 Issue 2, p684-701. 18p.
Subjects:	Nonlinear dynamical systems, Artificial neural networks, Adaptive control systems, Back propagation, Simulation methods & models, Lyapunov stability, Mean square algorithms
Abstract:	The paper describes a new neural network design, which is known as the Local Recurrent Sigma‐Pi Artificial Neural Network (LRSPANN), to model and control nonlinear dynamical systems. The given model includes local recurrent self‐feedback links in the hidden layer, which contribute to the dynamic memory and make it possible to effectively represent the behavior of the temporal system. The backpropagation learning algorithm is a gradient‐descent‐based method that is effectively used in updating network parameters and reducing modeling error. A Lyapunov‐based stability analysis is conducted to achieve reliable learning and closed‐loop stability. The effectiveness of the proposed LRSPANN is tested with the help of comparative simulations with Sigma‐Pi Artificial Neural Network (SPANN), Elman Recurrent Neural Network (ERNN), and Feed‐Forward Neural Network (FFNN). The proposed model has the lowest mean squared error (MSE) of 4.7×10−7$$ 4.7\times 1{0}^{-7} $$ in Example 1 and a mean squared error of 6.1×10−8$$ 6.1\times 1{0}^{-8} $$ in Example 2, which is better than any other compared network. These findings illustrate that the proposed methodology is the most accurate and efficient for modeling and controlling nonlinear systems. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	The paper describes a new neural network design, which is known as the Local Recurrent Sigma‐Pi Artificial Neural Network (LRSPANN), to model and control nonlinear dynamical systems. The given model includes local recurrent self‐feedback links in the hidden layer, which contribute to the dynamic memory and make it possible to effectively represent the behavior of the temporal system. The backpropagation learning algorithm is a gradient‐descent‐based method that is effectively used in updating network parameters and reducing modeling error. A Lyapunov‐based stability analysis is conducted to achieve reliable learning and closed‐loop stability. The effectiveness of the proposed LRSPANN is tested with the help of comparative simulations with Sigma‐Pi Artificial Neural Network (SPANN), Elman Recurrent Neural Network (ERNN), and Feed‐Forward Neural Network (FFNN). The proposed model has the lowest mean squared error (MSE) of 4.7×10−7$$ 4.7\times 1{0}^{-7} $$ in Example 1 and a mean squared error of 6.1×10−8$$ 6.1\times 1{0}^{-8} $$ in Example 2, which is better than any other compared network. These findings illustrate that the proposed methodology is the most accurate and efficient for modeling and controlling nonlinear systems. [ABSTRACT FROM AUTHOR]
ISSN:	01432087
DOI:	10.1002/oca.70094