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.
Publié le : 2004-07-05
Classification:
Ill-posed problems,
Heat equation,
Low-regret control,
Regularization,
Problems of incomplete data,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-00763938,
author = {Dorville, Ren\'e and Nakoulima, Ousseynou and Omrane, Abdennebi},
title = {Low-regret control of singular distributed systems: the ill-posed backwards heat problem},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00763938}
}
Dorville, René; Nakoulima, Ousseynou; Omrane, Abdennebi. Low-regret control of singular distributed systems: the ill-posed backwards heat problem. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00763938/