Global exact controllability in infinite time of Schr\"odinger equation
Vahagn Nersesyan (LM-Versailles), Hayk Nersisyan (AGM)
TL;DR
This paper proves that the Schrödinger equation can be exactly controlled in infinite time to reach any state, but not in finite time in lower Sobolev spaces, using an inverse mapping theorem.
Contribution
It establishes the exact controllability of the Schrödinger equation in infinite time and introduces a novel proof technique based on an inverse mapping theorem.
Findings
System is exactly controllable in infinite time to any position.
System is not exactly controllable in finite time in lower Sobolev spaces.
Proof utilizes an inverse mapping theorem for multivalued functions.
Abstract
In this paper, we study the problem of controllability of Schr\"odinger equation. We prove that the system is exactly controllable in infinite time to any position. The proof is based on an inverse mapping theorem for multivalued functions. We show also that the system is not exactly controllable in finite time in lower Sobolev spaces.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Nonlinear Differential Equations Analysis · Guidance and Control Systems