Optimal control for a controlled ill-posed wave equation without requiring the Slater hypothesis
Laboratory of Mathematics, Informatics and Systems, University of Larbi Tébessi
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.
Ill-posed wave equation, No-regret control, Incomplete data, Carleman estimates, Null-controllability.
|Directorate-General for Scientific Research and Technological Development
|This work was supported by the Directorate-General for Scientific Research and Technological Development (DGRSDT).
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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
\by Abdelhak Hafdallah
\paper Optimal control for a controlled ill-posed wave equation without requiring the Slater hypothesis
\jour Ural Math. J.
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