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On the semi-global stabilizability of the Korteweg-de Vries Equation via model predictive control

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2018

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Boulanger, Anne-Céline
Kunisch, Karl

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https://doi.org/10.1051/cocv/2017001
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ESAIM: Control, Optimisation and Calculus of Variations. EDP Sciences. 2018, 24(1), pp. 237-263. ISSN 1292-8119. eISSN 1262-3377. Available under: doi: 10.1051/cocv/2017001

Abstract

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.

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510 Mathematics

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Receding horizon Control, model predictive Control, asymptotic stability, infinite-dimensional systems

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ISO 690AZMI, Behzad, Anne-Céline BOULANGER, Karl KUNISCH, 2018. On the semi-global stabilizability of the Korteweg-de Vries Equation via model predictive control. In: ESAIM: Control, Optimisation and Calculus of Variations. EDP Sciences. 2018, 24(1), pp. 237-263. ISSN 1292-8119. eISSN 1262-3377. Available under: doi: 10.1051/cocv/2017001
BibTex
@article{Azmi2018semig-56312,
  year={2018},
  doi={10.1051/cocv/2017001},
  title={On the semi-global stabilizability of the Korteweg-de Vries Equation via model predictive control},
  number={1},
  volume={24},
  issn={1292-8119},
  journal={ESAIM: Control, Optimisation and Calculus of Variations},
  pages={237--263},
  author={Azmi, Behzad and Boulanger, Anne-Céline and Kunisch, Karl}
}
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