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

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2017 by IJMTT Journal
Volume-41 Number-3
Year of Publication : 2017
Authors : Abdelhak Hafdallah, Abdelhamid Ayadi, Chafia Laouar
  10.14445/22315373/IJMTT-V41P528

MLA

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). V41(3):283-288 January 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

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.

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