On the control of ill-posed distributed parameter systems

We show that the so-called low-regret (or least-regret) control by J. L. Lions [8] fits on the control of ill-posed problems. At each time, we give the characterization of the so-called no-regret control by means of singular optimality systems. For the backward heat ill-posed problem, no Slater hypo...

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Bibliographic Details
Published inESAIM. Proceedings Vol. 17; pp. 50 - 66
Main Authors Dorville, R., Nakoulima, O., Omrane, A.
Format Journal Article
LanguageEnglish
Published EDP Sciences 01.04.2007
Subjects
Dynamical Systems
Mathematics
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Summary:We show that the so-called low-regret (or least-regret) control by J. L. Lions [8] fits on the control of ill-posed problems. At each time, we give the characterization of the so-called no-regret control by means of singular optimality systems. For the backward heat ill-posed problem, no Slater hypothesis is assumed on the admissible set of controls ${{\cal U}_{\mbox{\tiny ad}}}$. This work is two pieces, and two methods are considered : the regularization method and the null-controllability method. For the first method, a zero order corrector is used, while for the second method, the passage to the limit is easy. The results presented here generalize the works in [2,3] to the no-regret control.
ISSN:1270-900X
1270-900X
DOI:10.1051/proc:071705