Robust Boundary Output-Feedback Control of a Reaction-Diffusion Equation with In-Domain Disturbances Robust Boundary Output-Feedback Control of a Reaction-Diffusion

Output feedback control design for a class of reaction-diffusion equations with Dirichlet anti-collocated sensing and actuation subject to in-domain disturbances is addressed. Within this setting, we design a finite-dimensional dynamic output feedback controller ensuring closed-loop exponential stab...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 206; no. 2
Main Authors Ferrante, Francesco, Shreim, Suha, Prieur, Christophe
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2025
Subjects
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
Partial differential equations
output feedback control
LMIs
robust control
Lyapunov methods
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ISSN0022-3239
1573-2878
DOI10.1007/s10957-025-02724-2

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Summary:Output feedback control design for a class of reaction-diffusion equations with Dirichlet anti-collocated sensing and actuation subject to in-domain disturbances is addressed. Within this setting, we design a finite-dimensional dynamic output feedback controller ensuring closed-loop exponential stability and input-output stability with an explicit estimate of the input-output gain. The approach is based on the spectral decomposition of the open-loop infinite-dimensional system and on the use of a suitable Lyapunov functional candidate. Sufficient conditions in the form of matrix inequalities are given to ensure closed-loop stability. These conditions are shown to be always feasible and are employed to devise an optimal controller design algorithm based on the solutions to some linear matrix inequalities.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-025-02724-2