ARTICLE
CONTROL OF SINGULAR DISTRIBUTED SYSTEMS BY CONTROLLABILITY: THE ILL-POSED BACKWARDS HEAT EQUATION.
- Far East Journal of Applied Mathematics , 118 (1) : 69-94
Lien de l'article :
http://dx.doi.org/10.17654/0972096025005
Discipline :
Mathématiques
Auteur(s) :
Billy André Guel, Sadou TAO, and Elie Ouedraogo
Auteur(s) tagués :
TAO Sadou
Renseignée par : TAO Sadou
Résumé
To deal with the ill-posed backwards heat equation, we propose
the controllability method. The point of view adopted consists in
interpreting the state equation as an inverse problem that allows us
to obtain a decoupled and strong singular optimality system for the
optimal control-state pair. This further permits to propose an existence
criterion for a regular solution of the backwards heat equation. It is
important to note that the results are obtained without recourse to a
Slater-type assumption.
Mots-clés
singular distributed systems, optimal control, ill-posed backwards heat equation, controllability, inverse problem.