Optimal control for the controllability of distributed systems of incomplete data. (Contrôle optimal pour les problèmes de contrôlabilité des systèmes distribués à données manquantes.) (French) Zbl 1085.49030
Summary: We are concerned with the null-controllability of the heat problem of incomplete initial data with a source term \(v \in L^2\). Then, we look for the best of controls \(v\) in the closed convex set of admissible controls \(\mathcal U_{\text{ad}}\) of \(L^2\). By the mean of the notion of low-regret controls of Lions, we obtain a singular optimality system without any supplementary hypothesis on \(\mathcal U_{\text{ad}}\).
MSC:
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 93B05 | Controllability |
| 93C20 | Control/observation systems governed by partial differential equations |
| 35K05 | Heat equation |
Keywords:
null-controllability; optimal control; low-regret control; optimality system; heat equationReferences:
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