|Publication ahead of print|
|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.
3 Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstraße 36, 8010 Graz, Austria, and Radon Institute, Austrian Academy of Sciences.
Corresponding author: firstname.lastname@example.org
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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