Finite-time stabilization output-feedback control of Schrödinger’s equation

In this paper, our objective is to achieve finite-time stabilization of Schrödinger’s equation using the method of switching observer functions. We propose a finite-time observer that matches the gain of the two switching functions. Subsequently, we use the backstepping to design a finite-time, output-feedback controller. Then, the finite-time stability of the resulting closed-loop system is proved. Finally, some numerical examples are given using the finite-element method. We see that the proposed controller is effective. The contribution of this paper is to extend the method of introducing the switching observer gain from the parabolic equation to achieve finite-time stabilization of Schrödinger’s equation. The open-loop system of the model we study is conservative. This helps to promote the development of control and stability theory, and provides new ideas and methods for applications in other fields.