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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2502.14999 |
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| _version_ | 1866913753198493696 |
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| author | Gherdaoui, Théo |
| author_facet | Gherdaoui, Théo |
| contents | We investigate the small-time local controllability (STLC) near the ground state of a bilinear Schrödinger 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 Schrödinger equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14999 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quadratic obstructions to Small-Time Local Controllability for the multi-input bilinear Schrödinger equation Gherdaoui, Théo Optimization and Control We investigate the small-time local controllability (STLC) near the ground state of a bilinear Schrödinger 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 Schrödinger equation. |
| title | Quadratic obstructions to Small-Time Local Controllability for the multi-input bilinear Schrödinger equation |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2502.14999 |