Sampled-Data Finite-Dimensional Boundary Control of 2-D Semilinear Parabolic Stochastic PDEs

• 成果类型: Article
• 署名作者: Wang, Pengfei; Fridman, Emilia
• 署名单位: Tel Aviv University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3514520
• 发表日期: 2025
• 页码: 3456-3463
• 关键词: Eigenvalues and eigenfunctions; Heating systems; DELAYS; Backstepping; shape; Closed loop systems; observers; noise; Indium tin oxide; control theory; 2-D PDEs; boundary control; sampled-data control; semilinear stochastic heat equation

摘要

This article addresses the sampled-data boundary stabilization of 2-D semilinear parabolic stochastic partial differential equation (PDEs) with globally Lipschitz nonlinearities. We consider Dirichlet actuation and design a finite-dimensional state-feedback controller with the shape functions in the form of eigenfunctions corresponding to the first N comparatively unstable eigenvalues. We extend the trigonometric change of variables to the 2-D case and further improve it, leading to a dynamic extension with the corresponding proportional-integral controller, where sampled-data control is implemented via a generalized hold device. By employing the corresponding Ito formulas for stochastic ordinary differential equation (ODEs) and PDEs, respectively, and suggesting a nontrivial stochastic extension of the descriptor method, we derive linear matrix inequalities (LMIs) for finding the controller dimension and gain that guarantees the global mean-square L-2 exponential stability for the full-order closed-loop system. A numerical example demonstrates the efficiency and advantage of our method.