RAPID STABILIZATION AND FINITE TIME STABILIZATION OF THE BILINEAR SCHRÖDINGER EQUATION - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2024

RAPID STABILIZATION AND FINITE TIME STABILIZATION OF THE BILINEAR SCHRÖDINGER EQUATION

Abstract

We propose a method to establish the rapid stabilization of the bilinear Schrödinger control system and its linearized system, and the finite time stabilization of the linearized system using the Grammian operators. The analysis of the rapid stabilization involves a new quantity (variable) which is inspired by the adjoint state in the optimal control theory and is proposed in our recent work on control systems associated with strongly continuous group. The analysis of the finite time stabilization follows the strategy introduced by Coron and Nguyen in the study of the finite time stabilization of the heat equation and incorporate a new ingredient involving the estimate of the cost of controls of the linearized system in small time derived in this paper.
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Dates and versions

hal-04577774 , version 1 (16-05-2024)

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  • HAL Id : hal-04577774 , version 1

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Hoai-Minh Nguyen. RAPID STABILIZATION AND FINITE TIME STABILIZATION OF THE BILINEAR SCHRÖDINGER EQUATION. 2024. ⟨hal-04577774⟩
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