Open Access
Review
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 44
Number of page(s) 49
DOI https://doi.org/10.1051/cocv/2024091
Published online 04 June 2025
  1. J.-M. Coron, Control and Nonlinearity. Mathematical Surveys and Monographs, Vol. 136 (2007). [Google Scholar]
  2. K. Beauchard and C. Laurent, Local controllability of 1D linear and nonlinear Schrodinger equations with bilinear control. J. Math. Pures Appl. 94 (2010) 520-554. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Bournissou, Local controllability of the bilinear 1D Schrodinger equation with simultaneous estimates. Math. Control Related Fields 13 (2023) 1047-1080. [CrossRef] [MathSciNet] [Google Scholar]
  4. M. Bournissou, Quadratic behaviors of the 1D linear Schrodinger equation with bilinear control. J. Diff. Equ. 351 (2023) 324-360. [CrossRef] [Google Scholar]
  5. J.M. Ball, J.E. Marsden and M. Slemrod, Controllability for distributed bilinear systems. SIAM J. Control Optim. 20 (1982) 575-597. [CrossRef] [MathSciNet] [Google Scholar]
  6. N. Boussaïd, M. Caponigro and T. Chambrion, Regular propagators of bilinear quantum systems. J. Funct. Anal. 278 (2020) 108412. [CrossRef] [MathSciNet] [Google Scholar]
  7. T. Chambrion and L. Thomann, A topological obstruction to the controllability of nonlinear wave equations with bilinear control term. SIAM J. Control Optim. 57 (2019) 2315-2327. [CrossRef] [MathSciNet] [Google Scholar]
  8. T. Chambrion and L. Thomann, On the bilinear control of the Gross-Pitaevskii equation. Ann. Inst. Henri Poincaré C Analyse non linéaire 37 (2020) 605-626. [CrossRef] [MathSciNet] [Google Scholar]
  9. K. Beauchard, Local controllability of a 1-D Schrödinger equation. J. Math. Pures Appl. 84 (2005) 851-956. [CrossRef] [MathSciNet] [Google Scholar]
  10. K. Beauchard and J.-M. Coron, Controllability of a quantum particle in a moving potential well. J. Funct. Anal. 232 (2006) 328-389. [Google Scholar]
  11. M. Morancey and V. Nersesyan, Global exact controllability of a 1D Schrödinger equations with a polarizability term. (2013). [Google Scholar]
  12. V. Nersesyan and H. Nersisyan, Global exact controllability in infinite time of Schrodinger equation. J. Math. Pures Appl. 97 (2010) 295-317. [Google Scholar]
  13. J.-M. Coron, On the small-time local controllability of a quantum particle in a moving one-dimensional infinite square potential well. Comp. Rend. Math. 342 (2006) 103-108. [Google Scholar]
  14. K. Beauchard and M. Morancey, Local controllability of 1D Schrödinger equations with bilinear control and minimal time. Math. Control Related Fields 4 (2014) 125-160. [CrossRef] [MathSciNet] [Google Scholar]
  15. K. Beauchard and F. Marbach, Quadratic obstructions to small-time local controllability for scalar-input systems. J. Diff. Equ. 264 (2018) 3704-3774. [CrossRef] [Google Scholar]
  16. F. Marbach, An obstruction to small time local null controllability for a viscous burgers' equation. Ann. Sci. Ecole normale supérieure 51 (2018) 1129-1177. [Google Scholar]
  17. K. Beauchard and F. Marbach, Unexpected quadratic behaviors for the small-time local null controllability of scalar-input parabolic equations. J. Math. Pures Appl. 136 (2020) 22-91. [Google Scholar]
  18. J.-M. Coron, A. Koenig and H.-M. Nguyen, On the small-time local controllability of a KdV system for critical lengths. J. Eur. Math. Soc. 26, 1193-1253. [Google Scholar]
  19. H.-M. Nguyen, Local controllability of the Korteweg-de Vries equation with the right Dirichlet control arXiv:2302.06237 (2023). [Google Scholar]
  20. E. Cerpa and E. Crépeau, Boundary controllability for the nonlinear Korteweg-de Vries equation on any critical domain. Ennales l'I.H.P. Anal. Nonlineaire 26 (2009) 457-475. [Google Scholar]
  21. J.-M. Coron and E. Crépeau, Exact boundary controllability of a nonlinear KdV equation with critical lengths. J. Eur. Math. Soc. 006 (2004) 367-398. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Bournissou, Small-time local controllability of the bilinear Schröodinger equation, despite a quadratic obstruction, thanks to a cubic term arXiv:hal-03600696 (2022). [Google Scholar]
  23. U. Boscain, M. Caponigro, T. Chambrion and M. Sigalotti, A weak spectral condition for the controllability of the bilinear Schrodinger equation with application to the control of a rotating planar molecule. Commun. Math. Phys. 311 (2012) 423-455. [CrossRef] [Google Scholar]
  24. T. Chambrion, P. Mason, M. Sigalotti and U.V. Boscain, Controllability of the discrete-spectrum Schrodinger equation driven by an external field. Ann. Institut Henri Poincare-analyse Non Lineaire 26 (2008) 329-349. [Google Scholar]
  25. S. Ervedoza and J.-P. Puel, Approximate controllability for a system of Schroödinger equations modeling a single trapped ion. Ann. Inst. Henri Poincare (C) Non Linear Analy. 26 (2009) 2111-2136. [CrossRef] [Google Scholar]
  26. V. Nersesyan, Global approximate controllability for Schröodinger equation in higher Sobolev norms and applications. Ann. Inst. Henri Poincare C, Anal. Non Lineaire 27 (2010) 901-915. [CrossRef] [MathSciNet] [Google Scholar]
  27. M. Sigalotti, P. Mason, U.V. Boscain and T. Chambrion, Generic controllability properties for the bilinear Schrödinger equation. Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference (2009) 3799-3804. [Google Scholar]
  28. K. Beauchard, J.-M. Coron and H. Teismann, Minimal time for the bilinear control of Schröodinger equations. Syst. Control Lett. 71 (2014) 1-6. [CrossRef] [Google Scholar]
  29. K. Beauchard, J.-M. Coron and H. Teismann, Minimal time for the approximate bilinear control of Schrodinger equations. Math. Methods Appl. Sci. 41 (2018). [Google Scholar]
  30. A. Duca and V. Nersesyan, Bilinear control and growth of Sobolev norms for the nonlinear Schröodinger equation. J. Eur. Math. Soc (2021). [Google Scholar]
  31. U. Boscain, K. Le Balc'h and M. Sigalotti, Schroödinger eigenfunctions sharing the same modulus and applications to the control of quantum systems (2024). working paper or preprint. arXiv:2403.08341 [Google Scholar]
  32. T. Chambrion and E. Pozzoli, Small-time bilinear control of Schröodinger equations with application to rotating linear molecules. Automatica 153 (2023) 111028. [CrossRef] [Google Scholar]
  33. A. Duca and E. Pozzoli, Small-time controllability for the nonlinear Schrödinger equation on ℝn via bilinear electromagnetic fields arXiv:2307.15819 (2024). [Google Scholar]
  34. H.J. Sussmann, A general theorem on local controllability. SIAM J. Control Optim. 25 (1987) 158-194. [CrossRef] [MathSciNet] [Google Scholar]
  35. R. Brockett, Controllability with quadratic drift. Math. Control Related Fields 3 (2013) 433-446. [CrossRef] [MathSciNet] [Google Scholar]
  36. M. Kawski, High-order small-time local controllability. Nonlinear Controllabil. Optimal Control 133 (2000). [Google Scholar]
  37. K. Beauchard and F. Marbach, A unified approach of obstructions to small-time local controllability for scalar-input systems arXiv:2205.14114 (2024). [Google Scholar]
  38. D. Krob, Codes limites et factorisations finies du monoïde libre. RAIRO Theoret. Inform. Appl. 21 (1987) 437-467. [CrossRef] [EDP Sciences] [Google Scholar]
  39. K. Beauchard, J. Le Borgne and F. Marbach, On expansions for nonlinear systems error estimates and convergence issues. Comp. Rend. Math. 361 (2023) 97-189. [CrossRef] [Google Scholar]
  40. H. Hermes and M. Kawski, Local controllability of a single input, affine system. Nonlinear Anal. Appl. (1987) 235-248. [Google Scholar]
  41. K. Beauchard, J. Le Borgne and F. Marbach, Growth of structure constants of free lie algebras relative to hall bases. J. Algebra 612 (2022) 281-378. [CrossRef] [MathSciNet] [Google Scholar]
  42. E. Cerpa, Exact controllability of a nonlinear Korteweg-—de Vries equation on a critical spatial domain. SIAM J. Control Optim. 46 (2007) 877-899. [CrossRef] [MathSciNet] [Google Scholar]
  43. A. Duca and V. Nersesyan, Local exact controllability of the 1D nonlinear Schrödinger equation in the case of Dirichlet boundary conditions. SIAM J. Control. Optim. 0 (2022). S20-S36. [Google Scholar]
  44. M. Morancey, Simultaneous local exact controllability of 1D bilinear Schrodinger equations. Ann. I.H.P. Anal. Non Linéaire 31 (2014) 501-529. [Google Scholar]
  45. G. Turinici, On the controllability of bilinear quantum systems. Mathematical models and methods for ab initio Quantum Chemistry, edited by M. Defranceschi and C. Le Bris, Vol. 74 of Lecture Notes in Chemistry, Springer (2000) 75-92. [CrossRef] [Google Scholar]

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