Quadratic obstructions to Small-Time Local Controllability for the multi-input bilinear Schr\"odinger equation
Optimization and Control
2025-03-25 v2
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.
Keywords
Cite
@article{arxiv.2502.14999,
title = {Quadratic obstructions to Small-Time Local Controllability for the multi-input bilinear Schr\"odinger equation},
author = {Théo Gherdaoui},
journal= {arXiv preprint arXiv:2502.14999},
year = {2025}
}
Comments
arXiv admin note: text overlap with arXiv:2407.07446