Exact controllability for the Schrödinger equation. (English) Zbl 0795.93018

Machtyngier, Elaine

SIAM J. Control Optimization 32, No. 1, 24-34 (1994).

Summary: The exact controllability of Schrödinger equation in bounded domains with Dirichlet boundary condition is studied. Both the boundary controllability and the internal controllability problems are considered. Concerning the boundary controllability, the paper proves the exact controllability in \(H^{-1}(\Omega)\) with \(L^ 2\)-boundary control. On the other hand, the exact controllability in \(L^ 2(\Omega)\) is proved with \(L^ 2\)-controls supported in a neighborhood of the boundary. Both results hold for an arbitrarily small time. The method of proof combines both the HUM (Hilbert Uniqueness Method) and multiplier techniques.

MSC:

93B05	Controllability
35B45	A priori estimates in context of PDEs
93C20	Control/observation systems governed by partial differential equations

Keywords:

Hilbert uniqueness method; exact controllability; Schrödinger equation