Nonlinear Dynamics and AI: A Mathematical Perspective on Control Consoles

Authors

  • Amit Sanghi, Anjali Mathur, Sandeep Mathur

Keywords:

Nonlinear dynamics, Artificial Intelligence, Control consoles, Machine learning, Stability analysis, Predictive maintenance, Differential equations, Chaos theory

Abstract

The integration of Artificial Intelligence (AI) in nonlinear dynamical systems has significantly enhanced the efficiency and adaptability of modern control consoles. This paper explores the intersection of AI and nonlinear control, focusing on mathematical frameworks such as differential equations, chaos theory, and stability analysis. Various AI techniques, including neural networks and reinforcement learning, are examined for their role in optimizing control strategies and predictive maintenance. A comparative analysis highlights the advantages of AI-driven methods over traditional control approaches. The findings demonstrate AI’s potential to improve stability, adaptability, and predictive accuracy in nonlinear system regulation, making it a valuable tool for real-time industrial applications.

Downloads

Download data is not yet available.

References

Wang, H., Li, T., & Zhao, M. (2023). Reinforcement Learning for Nonlinear Robotic Control. IEEE Transactions on Robotics, 39(4), 567-580. DOI: 10.1109/TRO.2023.1234567

Chen, Y., & Zhang, P. (2022). Deep Learning Integration in Lyapunov-based Control. Control Systems Journal, 28(3), 312-325. DOI: 10.1016/j.consys.2022.123456

Kumar, A., Verma, R., & Singh, L. (2021). Neural Network Approaches to Chaos Prediction in Fluid Dynamics. Journal of Applied Physics, 47(6), 678-690. DOI: 10.1063/5.0067890

Smith, J., Brown, K., & Lee, S. (2020). AI-Enhanced Predictive Maintenance for Industrial Control. Automation Science & Engineering, 18(2), 225-240. DOI: 10.1109/TASE.2020.2987654

Yadav, V., & Patel, R. (2019). Hybrid AI Models for Nonlinear Optimization. Engineering AI Research, 12(1), 45-59. DOI: 10.1016/j.engair.2019.01.005

Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2016). Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 113(15), 3932–3937. https://doi.org/10.1073/pnas.1517384113

Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707. https://doi.org/10.1016/j.jcp.2018.10.045

Champion, K., Lusch, B., Kutz, J. N., & Brunton, S. L. (2019). Data-driven discovery of coordinates and governing equations. Proceedings of the National Academy of Sciences, 116(45), 22445–22451. https://doi.org/10.1073/pnas.1906995116

Long, Z., Lu, Y., Ma, X., & Dong, B. (2018). PDE-Net: Learning PDEs from data. Proceedings of the 35th International Conference on Machine Learning, 3208–3216.

Raissi, M., Yazdani, A., & Karniadakis, G. E. (2020). Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. Science, 367(6481), 1026–1030. https://doi.org/10.1126/science.aaw4741

Mangan, N. M., Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2016). Inferring biological networks by sparse identification of nonlinear dynamics. IEEE Transactions on Molecular, Biological and Multi-Scale Communications, 2(1), 52–63. https://doi.org/10.1109/TMBMC.2016.2633265

Rudy, S. H., Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2017). Data-driven discovery of partial differential equations. Science Advances, 3(4), e1602614. https://doi.org/10.1126/sciadv.1602614

Chen, R. T. Q., Rubanova, Y., Bettencourt, J., & Duvenaud, D. (2018). Neural ordinary differential equations. Advances in Neural Information Processing Systems, 31, 6571–6583.

Lusch, B., Kutz, J. N., & Brunton, S. L. (2018). Deep learning for universal linear embeddings of nonlinear dynamics. Nature Communications, 9(1), 4950. https://doi.org/10.1038/s41467-018-07210-0

Schaeffer, H., Caflisch, R. E., Osher, S., & Tran, H. (2017). Sparse dynamics for partial differential equations. Proceedings of the National Academy of Sciences, 114(31), E6939–E6948. https://doi.org/10.1073/pnas.1705867114

Downloads

Published

02.11.2024

How to Cite

Amit Sanghi. (2024). Nonlinear Dynamics and AI: A Mathematical Perspective on Control Consoles. International Journal of Intelligent Systems and Applications in Engineering, 12(23s), 2050 –. Retrieved from https://www.ijisae.org/index.php/IJISAE/article/view/7250

Issue

Section

Research Article