On the control of ill-posed distributed parameter systems

Abstract : 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.
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René Dorville, Ousseynou Nakoulima, Abdennebi Omrane. On the control of ill-posed distributed parameter systems. ESAIM: Proceedings, EDP Sciences, 2007, 17, pp.50-66. ⟨hal-00720814⟩

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