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Article Dans Une Revue Journal of Functional Analysis Année : 2005

Controllability cost of conservative systems: resolvent condition and transmutation

Résumé

This article concerns the exact controllability of unitary groups on Hilbert spaces with unbounded control operator. It provides a necessary and sufficient condition not involving time which blends a resolvent estimate and an observability inequality. By the transmutation of controls in some time L for the corresponding second order conservative system, it is proved that the cost of controls in time T for the unitary group grows at most like \exp(\alpha L^{2}/T) as T tends to 0. In the application to the cost of fast controls for the Schrödinger equation, L is the length of the longest ray of geometric optics which does not intersect the control region. This article also provides observability resolvent estimates implying fast smoothing effect controllability at low cost, and underscores that the controllability cost of a system is not changed by taking its tensor product with a conservative system.

Dates et versions

hal-00002098 , version 1 (16-06-2004)

Identifiants

Citer

Luc Miller. Controllability cost of conservative systems: resolvent condition and transmutation. Journal of Functional Analysis, 2005, 218 (2), pp.425-444. ⟨10.1016/j.jfa.2004.02.001⟩. ⟨hal-00002098⟩
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