No-Regret Optimal Control Characterization for an Ill-Posed Wave Equation

Abdelhak Hafdallah; Abdelhamid Ayadi; Chafia Laouar

doi:https://doi.org/10.14445/22315373/IJMTT-V41P528

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 41 | Number 3 | Year 2017 | Article Id. IJMTT-V41P528 | DOI : https://doi.org/10.14445/22315373/IJMTT-V41P528

No-Regret Optimal Control Characterization for an Ill-Posed Wave Equation

Abdelhak Hafdallah, Abdelhamid Ayadi, Chafia Laouar

Abstract

In this paper, we give a characteriz- ation (optimality system) of a quadratic optimal control for an ill-posed wave equation without using the extra hypothesis of Slater (i.e . U_ad set of admissible controls has a non-empty interior). By using a parabolic regularization we get a missing data problem where we associate a no-regret control to obtain a singular optimality system, then we pass to limit and by a corrector of order zero we complete the information.

Keywords

Ill-posed wave equation, no-regret control, optimal control, parabolic regularization.

References

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Citation :

Abdelhak Hafdallah, Abdelhamid Ayadi, Chafia Laouar, "No-Regret Optimal Control Characterization for an Ill-Posed Wave Equation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 41, no. 3, pp. 283-288, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V41P528