The paper investigates the influence of optimization methods on the efficiency of an extremal control system based on acoustic anomaly detection. The proposed system can detect abnormal equipment operating modes by analyzing sound characteristics and automatically adapting control parameters to new operating conditions. Using mathematical modeling, the operation of the system with different optimization algorithms (gradient descent, Momentum, Nesterov and RMSProp) was studied. The results show that RMSProp provides the fastest transition to steady state (103 s) with minimal overshoot (3%), but there are significant oscillations in the control signal. Classic gradient descent demonstrates an acceptable stabilization time (123 s) with moderate overshoot (23%). The Momentum and Nesterov methods are characterized by the longest settling time (173 and 160 s, respectively). The study confirms the feasibility of using extremal control systems with adaptive optimization to improve the reliability and efficiency of technological equipment under variable operating conditions.
- Wang, H., Luo, Y., An, W., Sun, Q., Xu, J., & Zhang, L. (2020). PID controller-based stochastic optimization acceleration for deep neural networks. IEEE Transactions on Neural Networks and Learning Systems, 31(12), 5079–5091. https://doi.org/10.1109/TNNLS.2019.2963066.
- Trollberg, O. (2017). On Real-Time Optimization using Extremum Seeking Control and Economic Model Predictive Control. Doctoral thesis, KTH Royal Institute of Technology.
- Kaminskas V, Šidlauskas K, Tallat-Kelpša Č. (1991). Constrained self-tuning control of stochastic extremal systems. Informatica: An International Journal of Computing and Informatics. 2(1):33-52. doi:10.3233/INF-1991-2102.
- Mareels, I. M. Y., Anderson, B. D. O., Bitmead, R. R., Bodson, M., & Sastry, S. S. (1987). Revisiting the MIT rule for adaptive control. IFAC Proceedings Volumes, 20(2), 161–166. https://doi.org/10.1016/S1474-6670(17)55954-6
- Goh, G. (2017). Why momentum really works. Distill. https://doi.org/10.23915/distill.00006
- Alexandre d’Aspremont, Damien Scieur and Adrien Taylor. (2021). Acceleration Methods. Foundations and Trends® in Optimization, Vol. 5: No. 1-2, pp. 1-245. http://dx.doi.org/10.1561/2400000036
- Dauphin, Y., Vries, H., Chung, J., & Bengio, Y. (2015). Equilibrated adaptive learning rates for non-convex optimization. arXiv. https://arxiv.org/abs/1502.04390
- Saad-Falcon, A., Howard, C., Romberg, J., Allen, K. (2024). Level set methods for gradient‑free optimization of metasurface arrays. Scientific Reports, 14, 16674. doi: 10.1038/s41598-024-67142-2.