Hierarchical Control for the parabolic ill-posed Cauchy problem

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Résumé

This paper deals with the control problem of the parabolic ill-posed Cauchy system. To do this, we use a notion of hierarchical control inspired by the control of Stackelberg. This approach makes it possible to characterize the optimal control-state pair via a singular optimality system. And this, without using any additional assumptions, such as that of non-vacuity of the interior of the sets of admissible controls, an assumption that many analyses have had to use.

Mots-clés

Partial differential equations, Singular distributed systems, Ill-posed Cauchy problem, Optimal control, Hierarchical control, Singular optimality system