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Article Dans Une Revue Communications in Mathematical Physics Année : 2010

Controllability Issues for Continuous-Spectrum Systems and Ensemble Controllability of Bloch Equations

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Jean-Michel Coron
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Pierre Rouchon

Résumé

We study the controllability of the Bloch equation, for an ensemble of non interacting half-spins, in a static magnetic field, with dispersion in the Larmor frequency. This system may be seen as a prototype for infinite dimensional bilinear systems with continuous spectrum, whose controllability is not well understood. We provide several mathematical answers, with discrimination between approximate and exact controllability, and between finite time or infinite time controllability: this system is not exactly controllable in finite time T with bounded controls in L 2(0, T), but it is approximately controllable in L ∞ in finite time with unbounded controls in L-infinity-loc[0,.infinity). Moreover, we propose explicit controls realizing the asymptotic exact controllability to a uniform state of spin + 1/2 or −1/2.
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Dates et versions

hal-00475751 , version 1 (22-04-2010)

Identifiants

Citer

Karine Beauchard, Jean-Michel Coron, Pierre Rouchon. Controllability Issues for Continuous-Spectrum Systems and Ensemble Controllability of Bloch Equations. Communications in Mathematical Physics, 2010, 296 (2), pp.525-557. ⟨10.1007/s00220-010-1008-9⟩. ⟨hal-00475751⟩
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