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Ural Math. J., 2020, Volume 6, Issue 1, Pages 84–94 (Mi umj113)  

Optimal control for a controlled ill-posed wave equation without requiring the Slater hypothesis

Abdelhak Hafdallah

Laboratory of Mathematics, Informatics and Systems, University of Larbi Tébessi

Abstract: In this paper, we investigate the problem of optimal control for an ill-posed wave equation without using the extra hypothesis of Slater i.e. the set of admissible controls has a non-empty interior. Firstly, by a controllability approach, we make the ill-posed wave equation a well-posed equation with some incomplete data initial condition. The missing data requires us to use the no-regret control notion introduced by Lions to control distributed systems with incomplete data. After approximating the no-regret control by a low-regret control sequence, we characterize the optimal control by a singular optimality system.

Keywords: Ill-posed wave equation, No-regret control, Incomplete data, Carleman estimates, Null-controllability.

Funding Agency Grant Number
Directorate-General for Scientific Research and Technological Development
This work was supported by the Directorate-General for Scientific Research and Technological Development (DGRSDT).


DOI: https://doi.org/10.15826/umj.2020.1.007

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Citation: Abdelhak Hafdallah, “Optimal control for a controlled ill-posed wave equation without requiring the Slater hypothesis”, Ural Math. J., 6:1 (2020), 84–94

Citation in format AMSBIB
\Bibitem{Haf20}
\by Abdelhak Hafdallah
\paper Optimal control for a controlled ill-posed wave equation without requiring the Slater hypothesis
\jour Ural Math. J.
\yr 2020
\vol 6
\issue 1
\pages 84--94
\mathnet{http://mi.mathnet.ru/umj113}
\crossref{https://doi.org/10.15826/umj.2020.1.007}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=MR4128762}
\elib{https://elibrary.ru/item.asp?id=43793626}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85089118612}


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