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, Rue de Constantine 12002, Tébessa, Algeria)

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  ncomplete 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

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References


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DOI: http://dx.doi.org/10.15826/umj.2020.1.007

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