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<identifier>oai:HAL:hal-00720814v1</identifier>
<datestamp>2017-12-21</datestamp>
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<publisher>HAL CCSD</publisher>
<title lang=en>On the control of ill-posed distributed parameter systems</title>
<creator>Dorville, René</creator>
<creator>Nakoulima, Ousseynou</creator>
<creator>Omrane, Abdennebi</creator>
<contributor>Centre de Recherche en Economie, Gestion, Modélisation et Informatique Appliquée (CEREGMIA) ; Université des Antilles et de la Guyane (UAG)</contributor>
<contributor>Analyse Optimisation Controle (AOC) ; Université des Antilles et de la Guyane (UAG)</contributor>
<description>International audience</description>
<source>ISSN: 1270-900X</source>
<source>ESAIM: Proceedings</source>
<publisher>EDP Sciences</publisher>
<identifier>hal-00720814</identifier>
<identifier>https://hal.univ-antilles.fr/hal-00720814</identifier>
<identifier>https://hal.univ-antilles.fr/hal-00720814/document</identifier>
<identifier>https://hal.univ-antilles.fr/hal-00720814/file/esaimpr1.pdf</identifier>
<source>https://hal.univ-antilles.fr/hal-00720814</source>
<source>ESAIM: Proceedings, EDP Sciences, 2007, 17, pp.50-66</source>
<language>en</language>
<subject>[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>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 ${{cal U}_{mbox{ iny ad}}}$. 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.</description>
<date>2007-04</date>
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