Predictor methods for finite-dimensional observer-based control of stochastic parabolic PDEs
Abstract
We study output-feedback control of 1D stochastic semilinear heat equations with nonlinear multiplicative noise and uncertain time-varying input/output delays or sawtooth delays (that correspond to network-based control), where the nonlinearities satisfy globally Lipschitz condition. We assume that the input delay has a large constant known part 𝑟 . We consider Neumann actuation with non-local measurement. To compensate 𝑟 , we consider a chain of 𝑀 sub-predictors (conventional sub-predictors as in the deterministic case) and a novel chain of 𝑀 +1 sub-predictors, respectively, both in the form of ODEs that correspond to the delay fraction 𝑟 ∕ 𝑀 . For both cases, we construct Lyapunov functionals that depend on the deterministic and stochastic parts of the finite-dimensional part of the closed-loop systems, and employ the corresponding Itô’s formulas for stochastic ODEs and PDEs, respectively. We provide the mean-square 𝐿 2 exponential stability analysis of the full-order closed-loop system, leading to LMIs that are feasible for any 𝑟 provided 𝑀 and the observer dimension are large enough, and Lipschitz constants, as well as the upper bounds of unknown delays, are small enough. For the novel sub-predictors, we add an additional sub-predictor to the chain that leads to the closed-loop system with the stochastic infinite-dimensional tail and the stochastic finite-dimensional part where the delay fraction 𝑟 ∕ 𝑀 and the stochastic term appear in separate equations, which essentiall…
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- Authors
- Wang, P., & Fridman, E.
- Affiliations
- Tel Aviv University (IL)
- Corresponding author
- Wang, Pengfei
- Venue
- Systems & Control Letters
- Publisher
- Elsevier BV
- Published
- 2023-11
- Volume
- 181
- Pages
- 105632
- ISSN
- 0167-6911 (ISSN-L)
- OpenAlex
- W4387321702
- Cited by
- 6
- References
- 37
- Citations by year
- 2025: 2 · 2024: 4
- FWCI
- 0.66
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- Systems & Control Letters (publishedVersion)
- Funders
- Tel Aviv University
- Israel Science Foundation (673/19)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Controllability of Differential Equations
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Mathematics › Applied Mathematics › Nonlinear Differential Equations Analysis
- Keywords
- predictor-based control, output feedback control, semilinear heat equation, multiplicative noise, input delay compensation, network-based control, Lyapunov functional, mean-square exponential stability, linear matrix inequalities
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