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

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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