Quadratic obstructions to Small-Time Local Controllability for the multi-input bilinear Schr\"odinger equation

Théo Gherdaoui

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arXiv · 2502.14999

Quadratic obstructions to Small-Time Local Controllability for the multi-input bilinear Schr\"odinger equation

Théo Gherdaoui

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Abstract

We investigate the small-time local controllability (STLC) near the ground state of a bilinear Schr\"odinger equation when the linearized system is not controllable. It is well known that, for single-input systems, quadratic terms in the state expansion can then lead to obstructions to the STLC of the nonlinear system. In this work, we extend this phenomenon to the multi-input setting, presenting the first example of multi-input quadratic obstructions for PDEs. Our results build upon our previous study of such obstructions for ODEs and provide a functional framework for analyzing them in the bilinear Schr\"odinger equation.

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BibTeX RIS

Théo Gherdaoui. 2025-02-20. Quadratic obstructions to Small-Time Local Controllability for the multi-input bilinear Schr\"odinger equation. https://arxiv.org/abs/2502.14999

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