Well-posedness and exact controllability of fourth-order Schrödinger equation with hinged boundary control and collocated observation

In this paper, we consider the well-posedness and exact controllability of a fourth-order multi-dimensional Schrödinger equation with hinged boundary by either moment or Dirichlet boundary control and collocated observation, respectively. It is shown that in both cases, the systems are well posed in...

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Bibliographic Details
Published in:Mathematics of control, signals, and systems signals, and systems, 2016-09, Vol.28 (3), p.1, Article 22
Main Authors: Wen, Ruili, Chai, Shugen, Guo, Bao-Zhu
Format: Article
Language:English
Subjects:
Applied mathematics
Boundary conditions
Closed loop systems
Communications Engineering
Control
Mathematics
Mathematics and Statistics
Mechatronics
Networks
Original Article
Partial differential equations
Physics
Quantum physics
Robotics
Systems Theory
Theorems
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Summary:In this paper, we consider the well-posedness and exact controllability of a fourth-order multi-dimensional Schrödinger equation with hinged boundary by either moment or Dirichlet boundary control and collocated observation, respectively. It is shown that in both cases, the systems are well posed in the sense of D. Salamon, which implies that the systems are exactly controllable in some finite time interval if and only if its corresponding closed loop systems under the direct output proportional feedback are exponentially stable. This leads us to discuss further the exact controllability of the systems. In addition, the systems are consequently shown to be regular in the sense of G. Weiss as well, and the feedthrough operators are zero.
ISSN:0932-4194
1435-568X
DOI:10.1007/s00498-016-0175-4