Low-regret control of singular distributed systems: the ill-posed backwards heat problem

We use the low-regret notion of Lions for the control of a class of singular distributed systems: the ill-posed problems. A regularization approach is applied to the backwards heat equation, and we obtain a problem of incomplete data, for which the method of Nakoulima et al. is developed. Passing to...

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Bibliographic Details
Published inApplied mathematics letters pp. 549 - 552
Main Authors Dorville, René, Nakoulima, Ousseynou, Omrane, Abdennebi
Format Journal Article
LanguageEnglish
Published Elsevier 01.06.2004
Subjects
Analysis of PDEs
Mathematics
Ill-posed problems
Heat equation
Problems of incomplete data
Regularization
Low-regret control
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Summary:We use the low-regret notion of Lions for the control of a class of singular distributed systems: the ill-posed problems. A regularization approach is applied to the backwards heat equation, and we obtain a problem of incomplete data, for which the method of Nakoulima et al. is developed. Passing to the limit, a singular optimality system is obtained for the low-regret control of the original problem without any Slater hypothesis.
ISSN:0893-9659
DOI:10.1016/j.aml.2003.04.006