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Receding horizon control for the stabilization of the wave equation

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2018

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Kunisch, Karl

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https://doi.org/10.3934/dcds.2018021
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Discrete and Continuous Dynamical Systems. Series A (DCDS-A). American Institute of Mathematical Sciences (AIMS). 2018, 38(2), pp. 449-484. ISSN 1078-0947. eISSN 1553-5231. Available under: doi: 10.3934/dcds.2018021

Zusammenfassung

Stabilization of the wave equation by the receding horizon framework is investigated. Distributed control, Dirichlet boundary control, and Neumann boundary control are considered. Moreover for each of these control actions, the well-posedness of the control system and the exponential stability of Receding Horizon Control (RHC) with respect to a proper functional analytic setting are investigated. Observability conditions are necessary to show the suboptimality and exponential stability of RHC. Numerical experiments are given to illustrate the theoretical results.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Receding horizon control, model predictive control, asymptotic stability, observability, optimal control, infinite-dimensional systems.

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ISO 690AZMI, Behzad, Karl KUNISCH, 2018. Receding horizon control for the stabilization of the wave equation. In: Discrete and Continuous Dynamical Systems. Series A (DCDS-A). American Institute of Mathematical Sciences (AIMS). 2018, 38(2), pp. 449-484. ISSN 1078-0947. eISSN 1553-5231. Available under: doi: 10.3934/dcds.2018021
BibTex
@article{Azmi2018Reced-56313,
  year={2018},
  doi={10.3934/dcds.2018021},
  title={Receding horizon control for the stabilization of the wave equation},
  number={2},
  volume={38},
  issn={1078-0947},
  journal={Discrete and Continuous Dynamical Systems. Series A (DCDS-A)},
  pages={449--484},
  author={Azmi, Behzad and Kunisch, Karl}
}
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