Free Access
Issue
ESAIM: COCV
Volume 18, Number 4, October-December 2012
Page(s) 1207 - 1224
DOI https://doi.org/10.1051/cocv/2012004
Published online 27 March 2012
  1. A. Baciotti, Local Stabilizability of Nonlinear Control Systems. World Scientific, Singapore (1992).
  2. J.M. Ball and M. Slemrod, Feedback stabilization of distributed semilinear control systems. Appl. Math. Optim. 5 (1979) 169–179. [CrossRef] [MathSciNet]
  3. J.M. Ball, J.E. Mardsen and M. Slemrod, Controllability for distributed bilinear systems. SIAM J. Control Optim. 20 (1982) 575–597. [CrossRef] [MathSciNet]
  4. L. Baudouin and J. Salomon, Constructive solution of a bilinear optimal control problem for a Schrödinger equation. Syst. Control Lett. 57 (2008) 453–464. [CrossRef]
  5. K. Beauchard and C. Laurent, Local controllability of 1D linear and nonlinear Schrödinger equations with bilinear control. J. Math. Pures Appl. 94 (2010) 520–554. [CrossRef]
  6. P. Cannarsa and A.Y. Khapalov, Multiplicative controllability for reaction-diffusion equations with target states admitting finitely many changes of sign. Discrete Contin. Dyn. Syst. Ser. B 14 (2010) 1293–1311. [CrossRef] [MathSciNet]
  7. T. Chambrion, P. Mason, M. Sigalotti, and U. Boscain, Controllability of the discrete-spectrum Schrödinger equation driven by an external field. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26 (2009) 329–349. [CrossRef] [MathSciNet]
  8. J.M. Coron, On the small-time local controllability of a quantum particle in a moving one-dimensional infinite square potential well. C. R. Math. Acad. Sci. Paris 342 (2006) 103–108. [CrossRef] [MathSciNet]
  9. J.I. Díaz, J. Henry and A.M. Ramos, On the approximate controllability of some semilinear parabolic boundary-value problems. Appl. Math. Optim. 37 (1998) 71–97. [CrossRef] [MathSciNet]
  10. S. Ervedoza and J.P. Puel, Approximate controllability for a system of Schrödinger equations modeling a single trapped ion. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26 (2009) 2111–2136. [CrossRef]
  11. L.A. Fernández, Controllability of some semilinear parabolic problems with multiplicative control, presented at the Fifth SIAM Conference on Control and its applications, held in San Diego (2001).
  12. A. Friedman, Partial Differential Equations. Holt, Rinehart and Winston, New York (1969).
  13. A.Y. Khapalov, Mobile point controls versus locally distributed ones for the controllability of the semilinear parabolic equation. SIAM J. Control Optim. 40 (2001) 231–252. [CrossRef] [MathSciNet]
  14. A.Y. Khapalov, Controllability of the semilinear parabolic equation governed by a multiplicative control in the reaction term : A qualitative approach. SIAM J. Control. Optim. 41 (2003) 1886–1900. [CrossRef] [MathSciNet]
  15. A.Y. Khapalov, Controllability properties of a vibrating string with variable axial load. Discrete Contin. Dyn. Syst. 11 (2004) 311–324. [CrossRef] [MathSciNet]
  16. A.Y. Khapalov, Controllability of Partial Differential Equations Governed by Multiplicative Controls, edited by Springer Verlag. Lect. Notes Math. 1995 (2010).
  17. A.Y. Khapalov and R.R. Mohler, Reachable sets and controllability of bilinear time-invariant systems : A qualitative approach. IEEE Trans. Automat. Control 41 (1996) 1342–1346. [CrossRef] [MathSciNet]
  18. K. Kime, Simultaneous control of a rod equation and a simple Schrödinger equation. Syst. Control Lett. 24 (1995) 301–306. [CrossRef]
  19. O.A. Ladyzhenskaya, V.A. Solonnikov and N.N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type. Am. Math. Soc., Providence, RI (1968).
  20. S. Lenhart and M. Liang, Bilinear optimal control for a wave equation with viscous damping. Houston J. Math. 26 (2000) 575–595. [MathSciNet]
  21. M. Liang, Bilinear optimal control for a wave equation. Math. Models Methods Appl. Sci. 9 (1999) 45–68. [CrossRef]
  22. J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag (1971).
  23. S. Müller, Strong convergence and arbitrarily slow decay of energy for a class of bilinear control problems. J. Differ. Equ. 81 (1989) 50–67. [CrossRef] [MathSciNet]
  24. A.I. Prilepko, D.G. Orlovsky and I.A. Vasin, Methods for solving inverse problems in mathematical physics. Marcel Dekker Inc., New York (2000).
  25. R. Rink and R.R. Mohler, Completely controllable bilinear systems. SIAM J. Control 6 (1968) 477–486. [CrossRef] [MathSciNet]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.