OPTIMAL CONTROL FOR EVOLUTION PROBLEM OF INCOMPLETE DATA

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Résumé

In this work, we give a characterization of the control for ill-posed problems. We propose
a regularization method which consists of improving the data in order to obtain a well-posed problem.
The optimal control of the regularized system is discussed and the approximated optimality system
is presented. We pass to the limit and we obtain a singular optimality system for the low-regret.
We use the convergence of the low-regret control to the no-regret control for which we obtain a
characterization of the control for the original problem.

Mots-clés

Low-regret, no-regret, regularization technique