Nonlinear Dynamic Model for AI-Augmented Sustainable Energy System

Bharat Khushalani

doi:doi:10.11648/j.ijsge.20251402.16

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Nonlinear Dynamic Model for AI-Augmented Sustainable Energy System

Bharat Khushalani^*

Published in International Journal of Sustainable and Green Energy (Volume 14, Issue 2)

Received: 7 June 2025 Accepted: 23 June 2025 Published: 30 June 2025

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Abstract

This paper presents a novel approach to stabilizing the Duffing oscillator using a neural-inspired control policy based on the hyperbolic tangent function. The controller, though structurally simple, is interpreted as a one-layer neural network with explicitly defined weights and no need for training. Through this lens, we explore how artificial intelligence techniques can be adapted to deliver interpretable, energy-aware control for nonlinear dynamical systems. The system’s long-term behavior is analyzed using bifurcation diagrams, Poincare sections, and Lyapunov-based stability analysis. Simulation results show that the control law suppresses chaotic transitions, enforces global boundedness, and facilitates adaptive entrainment with external forcing. Time evolution of the Lyapunov function remains bounded and oscillatory with the function’s peaks and troughs giving no indication of runaway growth or divergence. A custom energy efficiency metric is also introduced, quantifying the system’s ability to retain input energy under feedback control. This energy efficiency metric presents an upward trend with increasing excitation, suggesting that the controller not only stabilizes the system but also facilitates more effective interaction with the external environment. Together, these results demonstrate the potential of embedded AI control to regulate nonlinear systems in a sustainable, robust, and explainable manner. The findings offer a foundation for future research in control-aware learning, physics-informed neural architectures, and real-time energy regulation.

Published in	International Journal of Sustainable and Green Energy (Volume 14, Issue 2)
DOI	10.11648/j.ijsge.20251402.16
Page(s)	126-133
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Duffing Oscillator, Nonlinear Dynamics, Neural-inspired Control, Lyapunov Stability, Global Boundedness, Energy Efficiency, Bifurcation, Poincare Map, AI for Sustainability, Tanh Activation

References

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[5]	Z.-P. Jiang and Y. Wang, “Input-to-state stability for discrete-time nonlinear systems,” Automatica, vol. 37, no. 6, pp. 857-869, 2001. https://doi.org/10.1016/S0005-1098(01)00028-0
[6]	M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Physics- informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,” J. Comput. Phys., vol. 378, pp. 686-707, Feb. 2019. https://doi.org/10.1016/j.jcp.2018.10.045
[7]	K. Doya, “Reinforcement learning in continuous time and space,” Neural Comput., vol. 12, no. 1, pp. 219-245, 2000. https://doi.org/10.1162/08997660030001596
[8]	M. W. Spong, S. Hutchinson, and M. Vidyasagar, Robot Modeling and Control. Hoboken, NJ, USA: Wiley, 2006. https://doi.org/10.1108/ir.2006.33.5.403.1
[9]	A. D. Ames, X. Xu, J. W. Grizzle, and P. Tabuada, “Control barrier function based quadratic programs for safety critical systems,” IEEE Trans. Autom. Control, vol. 62, no. 8, pp. 3861-3876, Aug. 2017.
[10]	D. Shi, Q. Zhang, M. Hong, F. Wang, S. Maslennikov, X. Luo, and Y. Chen, “Implementing deep reinforcement learning-based grid voltage control in real-world power systems: Challenges and insights,” arXiv preprint arXiv:2410.19880, Oct. 2024.
[11]	A. Bhan, D. Shi, and M. Krstic, “Neural operators for bypassing gain and control computations in PDE backstepping,” IEEE Transactions on Automatic Control, vol. 69, no. 8, pp. 5310-5325, Aug. 2024.
[12]	M. Krstic, A. Bhan, and D. Shi, “Neural operators of backstepping controller and observer gain functions for reaction-diffusion PDEs,” Automatica, vol. 164, p. 111649, 2024. https://doi.org/10.1016/j.automatica.2024.11164

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APA Style

Khushalani, B. (2025). Nonlinear Dynamic Model for AI-Augmented Sustainable Energy System. International Journal of Sustainable and Green Energy, 14(2), 126-133. https://doi.org/10.11648/j.ijsge.20251402.16

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ACS Style

Khushalani, B. Nonlinear Dynamic Model for AI-Augmented Sustainable Energy System. Int. J. Sustain. Green Energy 2025, 14(2), 126-133. doi: 10.11648/j.ijsge.20251402.16

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AMA Style

Khushalani B. Nonlinear Dynamic Model for AI-Augmented Sustainable Energy System. Int J Sustain Green Energy. 2025;14(2):126-133. doi: 10.11648/j.ijsge.20251402.16

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@article{10.11648/j.ijsge.20251402.16,
  author = {Bharat Khushalani},
  title = {Nonlinear Dynamic Model for AI-Augmented Sustainable Energy System
},
  journal = {International Journal of Sustainable and Green Energy},
  volume = {14},
  number = {2},
  pages = {126-133},
  doi = {10.11648/j.ijsge.20251402.16},
  url = {https://doi.org/10.11648/j.ijsge.20251402.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsge.20251402.16},
  abstract = {This paper presents a novel approach to stabilizing the Duffing oscillator using a neural-inspired control policy based on the hyperbolic tangent function. The controller, though structurally simple, is interpreted as a one-layer neural network with explicitly defined weights and no need for training. Through this lens, we explore how artificial intelligence techniques can be adapted to deliver interpretable, energy-aware control for nonlinear dynamical systems. The system’s long-term behavior is analyzed using bifurcation diagrams, Poincare sections, and Lyapunov-based stability analysis. Simulation results show that the control law suppresses chaotic transitions, enforces global boundedness, and facilitates adaptive entrainment with external forcing. Time evolution of the Lyapunov function remains bounded and oscillatory with the function’s peaks and troughs giving no indication of runaway growth or divergence. A custom energy efficiency metric is also introduced, quantifying the system’s ability to retain input energy under feedback control. This energy efficiency metric presents an upward trend with increasing excitation, suggesting that the controller not only stabilizes the system but also facilitates more effective interaction with the external environment. Together, these results demonstrate the potential of embedded AI control to regulate nonlinear systems in a sustainable, robust, and explainable manner. The findings offer a foundation for future research in control-aware learning, physics-informed neural architectures, and real-time energy regulation.
},
 year = {2025}
}

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TY  - JOUR
T1  - Nonlinear Dynamic Model for AI-Augmented Sustainable Energy System

AU  - Bharat Khushalani
Y1  - 2025/06/30
PY  - 2025
N1  - https://doi.org/10.11648/j.ijsge.20251402.16
DO  - 10.11648/j.ijsge.20251402.16
T2  - International Journal of Sustainable and Green Energy
JF  - International Journal of Sustainable and Green Energy
JO  - International Journal of Sustainable and Green Energy
SP  - 126
EP  - 133
PB  - Science Publishing Group
SN  - 2575-1549
UR  - https://doi.org/10.11648/j.ijsge.20251402.16
AB  - This paper presents a novel approach to stabilizing the Duffing oscillator using a neural-inspired control policy based on the hyperbolic tangent function. The controller, though structurally simple, is interpreted as a one-layer neural network with explicitly defined weights and no need for training. Through this lens, we explore how artificial intelligence techniques can be adapted to deliver interpretable, energy-aware control for nonlinear dynamical systems. The system’s long-term behavior is analyzed using bifurcation diagrams, Poincare sections, and Lyapunov-based stability analysis. Simulation results show that the control law suppresses chaotic transitions, enforces global boundedness, and facilitates adaptive entrainment with external forcing. Time evolution of the Lyapunov function remains bounded and oscillatory with the function’s peaks and troughs giving no indication of runaway growth or divergence. A custom energy efficiency metric is also introduced, quantifying the system’s ability to retain input energy under feedback control. This energy efficiency metric presents an upward trend with increasing excitation, suggesting that the controller not only stabilizes the system but also facilitates more effective interaction with the external environment. Together, these results demonstrate the potential of embedded AI control to regulate nonlinear systems in a sustainable, robust, and explainable manner. The findings offer a foundation for future research in control-aware learning, physics-informed neural architectures, and real-time energy regulation.

VL  - 14
IS  - 2
ER  -

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Author Information

Bharat Khushalani

Department of Artificial Intelligence, Shri Vishnu Engineering College for Women, Bhimavaram, India

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APA Style

Khushalani, B. (2025). Nonlinear Dynamic Model for AI-Augmented Sustainable Energy System. International Journal of Sustainable and Green Energy, 14(2), 126-133. https://doi.org/10.11648/j.ijsge.20251402.16

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ACS Style

Khushalani, B. Nonlinear Dynamic Model for AI-Augmented Sustainable Energy System. Int. J. Sustain. Green Energy 2025, 14(2), 126-133. doi: 10.11648/j.ijsge.20251402.16

Copy | Download

AMA Style

Khushalani B. Nonlinear Dynamic Model for AI-Augmented Sustainable Energy System. Int J Sustain Green Energy. 2025;14(2):126-133. doi: 10.11648/j.ijsge.20251402.16

Copy | Download

@article{10.11648/j.ijsge.20251402.16,
  author = {Bharat Khushalani},
  title = {Nonlinear Dynamic Model for AI-Augmented Sustainable Energy System
},
  journal = {International Journal of Sustainable and Green Energy},
  volume = {14},
  number = {2},
  pages = {126-133},
  doi = {10.11648/j.ijsge.20251402.16},
  url = {https://doi.org/10.11648/j.ijsge.20251402.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsge.20251402.16},
  abstract = {This paper presents a novel approach to stabilizing the Duffing oscillator using a neural-inspired control policy based on the hyperbolic tangent function. The controller, though structurally simple, is interpreted as a one-layer neural network with explicitly defined weights and no need for training. Through this lens, we explore how artificial intelligence techniques can be adapted to deliver interpretable, energy-aware control for nonlinear dynamical systems. The system’s long-term behavior is analyzed using bifurcation diagrams, Poincare sections, and Lyapunov-based stability analysis. Simulation results show that the control law suppresses chaotic transitions, enforces global boundedness, and facilitates adaptive entrainment with external forcing. Time evolution of the Lyapunov function remains bounded and oscillatory with the function’s peaks and troughs giving no indication of runaway growth or divergence. A custom energy efficiency metric is also introduced, quantifying the system’s ability to retain input energy under feedback control. This energy efficiency metric presents an upward trend with increasing excitation, suggesting that the controller not only stabilizes the system but also facilitates more effective interaction with the external environment. Together, these results demonstrate the potential of embedded AI control to regulate nonlinear systems in a sustainable, robust, and explainable manner. The findings offer a foundation for future research in control-aware learning, physics-informed neural architectures, and real-time energy regulation.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Nonlinear Dynamic Model for AI-Augmented Sustainable Energy System

AU  - Bharat Khushalani
Y1  - 2025/06/30
PY  - 2025
N1  - https://doi.org/10.11648/j.ijsge.20251402.16
DO  - 10.11648/j.ijsge.20251402.16
T2  - International Journal of Sustainable and Green Energy
JF  - International Journal of Sustainable and Green Energy
JO  - International Journal of Sustainable and Green Energy
SP  - 126
EP  - 133
PB  - Science Publishing Group
SN  - 2575-1549
UR  - https://doi.org/10.11648/j.ijsge.20251402.16
AB  - This paper presents a novel approach to stabilizing the Duffing oscillator using a neural-inspired control policy based on the hyperbolic tangent function. The controller, though structurally simple, is interpreted as a one-layer neural network with explicitly defined weights and no need for training. Through this lens, we explore how artificial intelligence techniques can be adapted to deliver interpretable, energy-aware control for nonlinear dynamical systems. The system’s long-term behavior is analyzed using bifurcation diagrams, Poincare sections, and Lyapunov-based stability analysis. Simulation results show that the control law suppresses chaotic transitions, enforces global boundedness, and facilitates adaptive entrainment with external forcing. Time evolution of the Lyapunov function remains bounded and oscillatory with the function’s peaks and troughs giving no indication of runaway growth or divergence. A custom energy efficiency metric is also introduced, quantifying the system’s ability to retain input energy under feedback control. This energy efficiency metric presents an upward trend with increasing excitation, suggesting that the controller not only stabilizes the system but also facilitates more effective interaction with the external environment. Together, these results demonstrate the potential of embedded AI control to regulate nonlinear systems in a sustainable, robust, and explainable manner. The findings offer a foundation for future research in control-aware learning, physics-informed neural architectures, and real-time energy regulation.

VL  - 14
IS  - 2
ER  -

Copy | Download