Boundary control of stochastic partial differential systems with delays and Lévy noise

IF 4.2 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2025-09-13 DOI:10.1016/j.jfranklin.2025.108055

K. Mathiyalagan , N. Soundarya Lakshmi , Yong-Ki Ma , Xiao-Heng Chang

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引用次数: 0

Abstract

This paper investigates the backstepping-based boundary control approach for stabilizing the semi-linear parabolic reaction-diffusion stochastic delayed partial differential system (SDPDS) driven by Lévy noise. The invertible Volterra integral transformation is chosen for transforming the original system to the target system. Boundary control for SDPDS is designed by finding the solution of PDE involving the kernel function with the help of method of successive approximation. By

(Q, S, R)

dissipative theory and linear matrix inequalities (LMIs), sufficient conditions are derived for proving the decreasing nature of the Lyapunov function for the target system. The result shows the system’s asymptotical stability under Neumann boundary conditions, further the stability of the target system proves the stability of the original system with control as our transformation is invertible. Finally, the proposed results are numerically validated.

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具有时滞和lsamvy噪声的随机偏微分系统的边界控制

研究了由lsamvy噪声驱动的半线性抛物型反应扩散随机时滞偏微分系统（SDPDS）的边界控制方法。将原系统转化为目标系统，采用可逆Volterra积分变换。利用逐次逼近法求解涉及核函数的偏微分方程，设计了SDPDS的边界控制。利用（Q，S，R）耗散理论和线性矩阵不等式，给出了证明目标系统Lyapunov函数的递减性质的充分条件。结果表明了系统在Neumann边界条件下的渐近稳定性，进一步证明了目标系统在控制下的稳定性，因为我们的变换是可逆的。最后，对所提结果进行了数值验证。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of The Franklin Institute-engineering and Applied Mathematics 工程技术-工程：电子与电气

CiteScore

7.30

自引率

14.60%

发文量

586

审稿时长

6.9 months

期刊介绍： The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.