Abstract
This paper addresses the sampled-data boundary stabilization of 2D semilinear parabolic stochastic 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 2D case and further improve it that leads 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 Itô formulas for stochastic ODEs and PDEs, respectively, and suggesting a non-trivial 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 L2 exponential stability for the full-order closed-loop system. A numerical example demonstrates the efficiency and advantage of our method.
Original language | English |
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Journal | IEEE Transactions on Automatic Control |
DOIs | |
State | Accepted/In press - 2024 |
Keywords
- 2D PDEs
- boundary control
- sampled-data control
- semilinear stochastic heat equation
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering