| Issue |
ESAIM: COCV
Volume 24, Number 1, January-March 2018
|
|
|---|---|---|
| Page(s) | 237 - 263 | |
| DOI | https://doi.org/10.1051/cocv/2017001 | |
| Published online | 19 January 2018 | |
On the semi-global stabilizability of the Korteweg-de Vries Equation via model predictive control★
1
Institute for Mathematics and Scientific Computing, University of Graz,
Heinrichstraße 36,
8010
Graz, Austria
2
Technische Universitat Munchen, Germany
anneceline.boulanger@gmail.com
3
Institute for Mathematics and Scientific Computing, University of Graz,
Heinrichstraße 36,
8010
Graz, Austria and Radon Institute, Austrian Academy of Sciences
karl.kunisch@uni-graz.at
a Corresponding author: behzad.azmi@uni-graz.at
Received:
20
April
2016
Revised:
29
December
2017
Accepted:
5
January
2017
Stabilization of the nonlinear Korteweg-de Vries (KdV) equation on a bounded interval by model predictive control (MPC) is investigated. This MPC strategy does not need any terminal cost or terminal constraint to guarantee the stability. The semi-global stabilizability is the key condition. Based on this condition, the suboptimality and exponential stability of the model predictive control are investigated. Finally, numerical experiment is presented which validates the theoretical results.
Mathematics Subject Classification: 49N35 / 93C20 / 93D20
Key words: Receding horizon control / model predictive control / asymptotic stability / infinite-dimensional systems
© EDP Sciences, SMAI 2018
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