Simultaneous control of a rod equation and a simple Schrödinger equation. (English) Zbl 0877.93003
Summary: We show that a corollary of a local approximate controllability result for the bilinear rod equation obtained previously is that the controls which “steer” the modes of the rod equation also move the modes of a controlled Schrödinger equation. Specifying a target point for the Schrödinger system restricts but does not determine the outcome of the controlled rod equation. The local result is a special case of a general local result for hyperbolic systems, to obtain a global approximate controllability result. After modifying the latter, we obtain a global result for the two systems.
MSC:
| 93B05 | Controllability |
| 93C20 | Control/observation systems governed by partial differential equations |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
Keywords:
controllability; Rod equation; Schrödinger equation; Phase shift; Local control; linear systemReferences:
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