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

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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]
Copyright of Optimal Control - Applications & Methods is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: Local Recurrent Sigma Pi Artificial Neural Network‐Based Adaptive Control of Nonlinear Dynamical Systems.
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  Data: <searchLink fieldCode="AR" term="%22Saini%2C+Kartik%22">Saini, Kartik</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> kartiksaini17@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Kumar%2C+Narendra%22">Kumar, Narendra</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Bhushan%2C+Bharat%22">Bhushan, Bharat</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Kumar%2C+Rajesh%22">Kumar, Rajesh</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Optimal+Control+-+Applications+%26+Methods%22">Optimal Control - Applications & Methods</searchLink>. Mar2026, Vol. 47 Issue 2, p684-701. 18p.
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  Data: <searchLink fieldCode="DE" term="%22Nonlinear+dynamical+systems%22">Nonlinear dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+neural+networks%22">Artificial neural networks</searchLink><br /><searchLink fieldCode="DE" term="%22Adaptive+control+systems%22">Adaptive control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Back+propagation%22">Back propagation</searchLink><br /><searchLink fieldCode="DE" term="%22Simulation+methods+%26+models%22">Simulation methods & models</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+stability%22">Lyapunov stability</searchLink><br /><searchLink fieldCode="DE" term="%22Mean+square+algorithms%22">Mean square algorithms</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Optimal Control - Applications & Methods is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1002/oca.70094
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      – Code: eng
        Text: English
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        PageCount: 18
        StartPage: 684
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      – SubjectFull: Nonlinear dynamical systems
        Type: general
      – SubjectFull: Artificial neural networks
        Type: general
      – SubjectFull: Adaptive control systems
        Type: general
      – SubjectFull: Back propagation
        Type: general
      – SubjectFull: Simulation methods & models
        Type: general
      – SubjectFull: Lyapunov stability
        Type: general
      – SubjectFull: Mean square algorithms
        Type: general
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      – TitleFull: Local Recurrent Sigma Pi Artificial Neural Network‐Based Adaptive Control of Nonlinear Dynamical Systems.
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            NameFull: Saini, Kartik
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            NameFull: Kumar, Narendra
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            NameFull: Bhushan, Bharat
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            – D: 01
              M: 03
              Text: Mar2026
              Type: published
              Y: 2026
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