Boundary Output Feedback Stabilization of the Linearized Schrödinger Equation with Nonlocal Term

Abstract

In this paper, we are concerned with the boundary output feedback stabilization problem of a Schrödinger equation with a nonlocal term. Firstly, we design an explicit boundary state feedback controller by backstepping approach. Under this controller, the closed-loop system is proved to be exponentially stable from the equivalence between the original system and the target system. Then, we propose an observer-based output feedback controller by replacing the state in state feedback controller with its estimation. The resulting closed-loop system admits a unique solution which is exponentially stable. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed feedback controller.

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Correspondence to Feng-Fei Jin.

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Recommended by Associate Editor Jun Cheng under the direction of Editor PooGyeon Park. This work was supported by the National Natural Science Foundation of China (Grant No. 62073203, 61603226).

Liping Wang received her M.S. degree from the School of Mathematics and Statistics, Shandong Normal University, Jinan, China in 2020. She studied distributed parameter systems control during master’s degree. She is currently studying for a doctorate at Shandong Normal University, Jinan, China.

Feng-Fei Jin received his Ph.D. degree from the Academy of Mathematics and Systems Science, Academia Sinica, Beijing, China in 2011. He was a postdoctoral fellow at the University of the Witwatersrand, South Africa during 2011–2012 and 2013–2015. He is currently with the Shandong Normal University, Jinan, China. His research interest focuses on distributed parameter systems control.

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Wang, L., Jin, FF. Boundary Output Feedback Stabilization of the Linearized Schrödinger Equation with Nonlocal Term. Int. J. Control Autom. Syst. (2021). https://doi.org/10.1007/s12555-019-1048-7

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Keywords

  • Backstepping transformation
  • boundary control
  • nonlocal term
  • output feedback
  • Schrödinger equation