Stochastic Model Predictive Control of Cheer Spikes and Low-Frequency Noise in Outdoor Festivals
DOI:
https://doi.org/10.14419/c1y1ch19Published
14-10-2025Keywords:
Stochastic Differential Equations; Model Predictive Control; Noise Suppression; Poisson Process; Wiener ProcessAbstract
This study addresses an open challenge in control systems—real-time suppression of random noise with jump and diffusion components—by proposing a method using Poisson- and Wiener-driven stochastic differential equations (SDEs) with model predictive control (MPC) for outdoor festivals. Achieving over 90% suppression of cheer spikes (1–5 kHz) and low-frequency noise (0.1–1 kHz), the approach introduces a novel extension of linear SDEs with Van der Pol and Duffing-type nonlinear SDEs, ensuring stability via a rigorously proven stochastic Lyapunov function. Detailed analyses of computational cost, robustness, and chaotic control, grounded in classical mathematical rigor, address real-time challenges. Visualization in time and frequency domains validates practical utility in acoustics engineering, offering a new paradigm for control systems. Recent studies have explored dynamical system responses under combined Poisson and Gaussian white noises, providing insights into their complex behaviors [14]. Furthermore, advancements in stochastic model predictive control have extended to handling sub-Gaussian noise, enhancing robustness in uncertain environments [7, 2, 5].
References
D. Applebaum. Levy Processes and Stochastic Calculus. Cambridge University Press, 2 edition, 2009.
Tahereh Bahraini and Alireza Naeimi-Sadigh. Active noise cancellation gets a boost: A novel diffusion-based approach in spline adaptive filters. ISA Transactions, 155:286–299, 2024.
Lihua Bai and Jin Ma. Stochastic differential equations driven by fractional brownian motion and poisson point process. Bernoulli, 21(1):303–334, 2015.
J. Guckenheimer and P. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, 1983.
Yao Jiang, Shuming Chen, Hao Meng, and Wei Li. A novel adaptive step-size hybrid active noise control system. Applied Acoustics, 182:108285, 2021.
J. F. C. Kingman. Poisson Processes. Oxford University Press, 1993.
Sen M. Kuo, Yi-Rou Chen, Cheng-Yuan Chang, and Chien-Wen Lai. Development and evaluation of light-weight active noise cancellation earphones. Applied Sciences, 8(7):1178, 2018.
H. J. Kushner. Stochastic Stability and Control. Academic Press, 2002.
X. Liu and Z. Liu. Poisson stable solutions for stochastic differential equations with l´evy noise. arXiv preprint arXiv:2002.00395, 2020.
X. Mao. Stochastic Differential Equations and Applications. Horwood Publishing, 2 edition, 2007.
B. Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer, 6 edition, 2003.
P. E. Protter. Stochastic Integration and Differential Equations. Springer, 2 edition, 2005.
P. Sopasakis et al. Nonlinear model predictive control for stochastic differential equation systems. IFAC-PapersOnLine, 50(1):10462– 10467, 2017.
T. Tripura and S. Chakraborty. Model-agnostic stochastic model predictive control. arXiv preprint arXiv:2211.13012, 2022.
A. Varga and H. J. M. Steeneken. Noisex-92: A database of noise signals, 1993. Available at http://www.speech.cs.cmu.edu/comp.speech/Section1/Data/noisex.html.