Control of Singular Distributed Systems by Controllability: The Ill-Posed Backwards Heat Equation

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Résumé

This paper deals with the ill-posed backwards heat equation. To do this, we propose the controllability method. The point of view adopted, which consists in interpreting the state equation as an inverse problem, allows us to obtain a decoupled and strong singular optimality system for the optimal control-state pair, but also to propose an existence criteria for a regular solution of the backwards heat equation. It is important to note that this results are obtained without recourse to a Slater-type assumption, an assumption to which many analyses have had to recourse.

Mots-clés

Singular distributed systems, Optimal control, Ill-posed backwards heat equation, Controllability, Inverse problem