| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 43 | |
| Number of page(s) | 29 | |
| DOI | https://doi.org/10.1051/cocv/2024032 | |
| Published online | 24 May 2024 | |
Stabilizability for nonautonomous linear parabolic equations with actuators as distributions
1
Institute for Mathematics and Scientic Computing, Karl-Franzens University of Graz, Heinrichstr. 36, 8010 Graz, Austria
2
Johann Radon Institute for Computational and Applied Mathematics, ÖAW, Altenbergerstraße 69, 4040 Linz, Austria
3
Institute for Mathematics, Humboldt University, Rudower Chaussee 25, 10117 Berlin, Germany
* Corresponding author: sergio.rodrigues@ricam.oeaw.ac.at
Received:
17
August
2023
Accepted:
4
April
2024
The stabilizability of a general class of abstract parabolic-like equations is investigated, with a finite number of actuators. This class includes the case of actuators given as delta distributions located at given points in the spatial domain of concrete parabolic equations. A stabilizing feedback control operator is constructed and given in explicit form. Then, an associated optimal control is considered and the corresponding Riccati feedback is investigated. Results of simulations are presented showing the stabilizing performance of both explicit and Riccati feedbacks.
Mathematics Subject Classification: 93D15 / 93B52 / 93C20 / 35K58
Key words: Stabilizing feedback controls / delta distribution actuators / parabolic equations / finite-dimensional control
© The authors. Published by EDP Sciences, SMAI 2024
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