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Polynomial chaos expansion and feature-space regression surrogates for stabilization of uncertain coupled PDE–ODE reactor processes
Publikationstyp
Journal Article
Date Issued
2026-06-23
Sprache
English
Author(s)
Journal
Volume
164
Article Number
103769
Citation
Journal of Process Control 164: 103769 (2026)
Publisher DOI
Publisher
Elsevier
Coupled PDE–ODE models arise naturally in process systems where a spatially distributed transport mechanism interacts with a lumped actuator, sensor, or well-mixed unit. In many such systems, reaction and coupling coefficients are not known exactly, and the resulting closed-loop must remain stable under parametric uncertainty. This paper studies a class of uncertain reaction–diffusion PDEs bidirectionally coupled with finitedimensional ODE dynamics through a spatial average and a spatially uniform injection term. The uncertainty is modeled by a time-invariant random vector with known distribution and is propagated through a polynomial chaos expansion (PCE), yielding a deterministic lifted surrogate that preserves the PDE–ODE interconnection structure. For this surrogate, we design constant deterministic feedback gains acting through both a direct ODE input and a Neumann boundary input proportional to the PDE spatial average. Using an energy method and a Poincaré-type inequality, we derive tractable linear matrix inequality conditions that ensure exponential stability of the lifted surrogate and, under an explicit truncation transfer condition, mean-square exponential stability of the original stochastic system. To accommodate nonlinear or partially unknown ODE-to-PDE coupling, we also introduce a feature-space ridge regression surrogate and quantify how the approximation error enlarges the coupling bound in the stability conditions. An observer-based output-feedback extension is established through a composite Lyapunov argument. Finally, a numerical range certificate is derived for the feature-space regression surrogate to diagnose non-normal transient behavior and, when the numerical abscissa is negative, to certify a sharper local contraction rate.
Subjects
Uncertain PDE–ODE systems
Boundary control
Polynomial chaos expansion
Mean-square exponential stability
Feature-space ridge regression
Reaction–diffusion systems
DDC Class
600: Technology