Geodesic
Optimal control for a controlled ill-posed wave equation without requiring the Slater hypothesis
Ural mathematical journal, Tome 6 (2020) no. 1, pp. 84-94

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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, Null-controllability.
Mots-clés : Carleman estimates 
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     author = {Abdelhak Hafdallah},
     title = {Optimal control for a controlled ill-posed wave equation without requiring the {Slater} hypothesis},
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     number = {1},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2020_6_1_a6/}
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Abdelhak Hafdallah. Optimal control for a controlled ill-posed wave equation without requiring the Slater hypothesis. Ural mathematical journal, Tome 6 (2020) no. 1, pp. 84-94. http://geodesic.mathdoc.fr/item/UMJ_2020_6_1_a6/