OPTIMAL CONTROL FOR A CONTROLLED ILL-POSED WAVE EQUATION WITHOUT REQUIRING THE SLATER HYPOTHESIS

Abdelhak Hafdallah
2020 Ural Mathematical Journal  
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
more » ... fter approximating the no-regret control by a low-regret control sequence, we characterize the optimal control by a singular optimality system.
doi:10.15826/umj.2020.1.007 fatcat:4asruix7rfbrxoefkl4l7awuzi