Geodesic
On the control of ill-posed distributed parameter systems
R. Dorville1 ; O. Nakoulima2 ; A. Omrane3
1 Université Antilles-Guyane, Laboratoire d'Analyse, Optimisation et Contrôle (AOC), UFR Sciences Exactes et Naturelles, Campus de Fouillole, 97159 Pointe à Pitre. E-mail: rene.dor@wanadoo.fr
2 onakouli@univ-ag.fr
3 aomrane@univ-ag.fr
ESAIM. Proceedings, Tome 17 (2007), pp. 50-66.

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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 . 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.
DOI : 10.1051/proc:071705

R. Dorville 1 ; O. Nakoulima 2 ; A. Omrane 3

1 Université Antilles-Guyane, Laboratoire d'Analyse, Optimisation et Contrôle (AOC), UFR Sciences Exactes et Naturelles, Campus de Fouillole, 97159 Pointe à Pitre. E-mail: rene.dor@wanadoo.fr
2 onakouli@univ-ag.fr
3 aomrane@univ-ag.fr 
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R. Dorville; O. Nakoulima; A. Omrane. On the control of ill-posed distributed parameter systems. ESAIM. Proceedings, Tome 17 (2007), pp. 50-66. doi : 10.1051/proc:071705. http://geodesic.mathdoc.fr/articles/10.1051/proc:071705/

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