Free Access
Volume 14, Number 1, January-March 2008
Page(s) 105 - 147
Published online 21 September 2007
  1. F. Albertini and D. D'Alessandro, Notions of controllability for bilinear multilevel quantum systems. IEEE Trans. Automat. Control 48 (2003) 1399–1403. [CrossRef] [MathSciNet] [Google Scholar]
  2. S. Alinhac and P. Gérard, Opérateurs pseudo-différentiels et théorème de Nash-Moser. Intereditions (Paris), collection Savoirs actuels (1991). [Google Scholar]
  3. C. Altafini, Controllability of quantum mechanical systems by root space decomposition of su(n). J. Math. Phys. 43 (2002) 2051–2062. [CrossRef] [MathSciNet] [Google Scholar]
  4. J.M. Ball, J.E. Marsden and M. Slemrod, Controllability for distributed bilinear systems. SIAM J. Control Optim. 20 (1982). [Google Scholar]
  5. L. Baudouin, A bilinear optimal control problem applied to a time dependent Hartree-Fock equation coupled with classical nuclear dynamics. Portugaliae Matematica (N.S.) 63 (2006) 293–325. [Google Scholar]
  6. L. Baudouin and J. Salomon, Constructive solution of a bilinear control problem. C.R. Math. Acad. Sci. Paris 342 (2006) 119–124. [CrossRef] [MathSciNet] [Google Scholar]
  7. L. Baudouin, O. Kavian and J.-P. Puel, Regularity for a Schrödinger equation with singular potential and application to bilinear optimal control. J. Differential Equations 216 (2005) 188–222. [CrossRef] [MathSciNet] [Google Scholar]
  8. K. Beauchard, Local controllability of a 1-D beam equation. SIAM J. Control Optim. (to appear). [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. Functional Analysis 232 (2006) 328–389. [Google Scholar]
  11. R. Brockett, Lie theory and control systems defined on spheres. SIAM J. Appl. Math. 25 (1973) 213–225. [CrossRef] [MathSciNet] [Google Scholar]
  12. E. Cancès, C. Le Bris and M. Pilot, Contrôle optimal bilinéaire d'une équation de Schrödinger. C.R. Acad. Sci. Paris, Série I 330 (2000) 567–571. [Google Scholar]
  13. J.-M. Coron, Global asymptotic stabilization for controllable systems without drift. Math. Control Signals Systems 5 (1992) 295–312. [CrossRef] [MathSciNet] [Google Scholar]
  14. J.-M. Coron, Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles bidimensionnels. C. R. Acad. Sci. Paris 317 (1993) 271–276. [Google Scholar]
  15. J.-M. Coron, On the controllability of 2-D incompressible perfect fluids. J. Math. Pures Appl. 75 (1996) 155–188. [Google Scholar]
  16. J.-M. Coron, Local Controllability of a 1-D Tank Containing a Fluid Modeled by the shallow water equations. ESAIM: COCV 8 (2002) 513–554. [CrossRef] [EDP Sciences] [Google Scholar]
  17. J.-M. Coron, On the small-time local controllability of a quantum particule in a moving one-dimensional infinite square potential well. C.R. Acad. Sci., Série I 342 (2006) 103–108. [Google Scholar]
  18. J.-M. Coron and E. Crépeau, Exact boundary controllability of a nonlinear KdV equation with critical lengths. J. Eur. Math. Soc. 6 (2004) 367–398. [Google Scholar]
  19. J.-M. Coron and A. Fursikov, Global exact controllability of the 2D Navier-Stokes equation on a manifold without boundary. Russ. J. Math. Phys. 4 (1996) 429–448. [Google Scholar]
  20. A.V. Fursikov and O.Yu. Imanuvilov, Exact controllability of the Navier-Stokes and Boussinesq equations. Russian Math. Surveys 54 (1999) 565–618. [CrossRef] [MathSciNet] [Google Scholar]
  21. O. Glass, On the controllability of the 1D isentropic Euler equation. J. European Mathematical Society 9 (2007) 427–486. [Google Scholar]
  22. O. Glass, Exact boundary controllability of 3-D Euler equation. ESAIM: COCV 5 (2000) 1–44. [CrossRef] [EDP Sciences] [Google Scholar]
  23. O. Glass, On the controllability of the Vlasov-Poisson system. J. Differential Equations 195 (2003) 332–379. [CrossRef] [MathSciNet] [Google Scholar]
  24. G. Gromov, Partial Differential Relations. Springer-Verlag, Berlin-New York-London (1986). [Google Scholar]
  25. A. Haraux, Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire. J. Math. Pures Appl. 68 (1989) 457–465. [MathSciNet] [Google Scholar]
  26. L. Hörmander, On the Nash-Moser Implicit Function Theorem. Annales Academiae Scientiarum Fennicae (1985) 255–259. [Google Scholar]
  27. T. Horsin, On the controllability of the Burgers equation. ESAIM: COCV 3 (1998) 83–95. [CrossRef] [EDP Sciences] [Google Scholar]
  28. R. Ilner, H. Lange and H. Teismann, Limitations on the control of Schrödinger equations. ESAIM: COCV 12 (2006) 615–635. [CrossRef] [EDP Sciences] [Google Scholar]
  29. T. Kato, Perturbation Theory for Linear operators. Springer-Verlag, Berlin, New-York (1966). [Google Scholar]
  30. W. Krabs, On moment theory and controllability of one-dimensional vibrating systems and heating processes. Springer – Verlag (1992). [Google Scholar]
  31. I. Lasiecka and R. Triggiani, Optimal regularity, exact controllability and uniform stabilization of Schrödinger equations with Dirichlet controls. Differential Integral Equations 5 (1992) 571–535. [Google Scholar]
  32. I. Lasiecka, R. Triggiani and X. Zhang, Global uniqueness, observability and stabilization of nonconservative Schrödinger equations via pointwise Carlemann estimates. J. Inverse Ill Posed-Probl. 12 (2004) 183–231. [MathSciNet] [Google Scholar]
  33. G. Lebeau, Contrôle de l'équation de Schrödinger. J. Math. Pures Appl. 71 (1992) 267–291. [MathSciNet] [Google Scholar]
  34. Machtyngier, Exact controllability for the Schrödinger equation. SIAM J. Contr. Opt. 32 (1994) 24–34. [Google Scholar]
  35. M. Mirrahimi and P. Rouchon, Controllability of quantum harmonic oscillators. IEEE Trans. Automat. Control 49 (2004) 745–747. [CrossRef] [MathSciNet] [Google Scholar]
  36. E. Sontag, Control of systems without drift via generic loops. IEEE Trans. Automat. Control 40 (1995) 1210–1219. [CrossRef] [MathSciNet] [Google Scholar]
  37. G. Turinici, On the controllability of bilinear quantum systems, in Mathematical Models and Methods for Ab Initio Quantum Chemistry, C. Le Bris and M. Defranceschi Eds., Lect. Notes Chemistry 74, Springer (2000). [Google Scholar]
  38. E. Zuazua, Remarks on the controllability of the Schrödinger equation. CRM Proc. Lect. Notes 33 (2003) 193–211. [Google Scholar]

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