Volume 18, Number 4, October-December 2012
|Page(s)||1207 - 1224|
|Published online||27 March 2012|
- A. Baciotti, Local Stabilizability of Nonlinear Control Systems. World Scientific, Singapore (1992).
- J.M. Ball and M. Slemrod, Feedback stabilization of distributed semilinear control systems. Appl. Math. Optim. 5 (1979) 169–179. [CrossRef] [MathSciNet]
- J.M. Ball, J.E. Mardsen and M. Slemrod, Controllability for distributed bilinear systems. SIAM J. Control Optim. 20 (1982) 575–597. [CrossRef] [MathSciNet]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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).
- A. Friedman, Partial Differential Equations. Holt, Rinehart and Winston, New York (1969).
- 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]
- 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]
- A.Y. Khapalov, Controllability properties of a vibrating string with variable axial load. Discrete Contin. Dyn. Syst. 11 (2004) 311–324. [CrossRef] [MathSciNet]
- A.Y. Khapalov, Controllability of Partial Differential Equations Governed by Multiplicative Controls, edited by Springer Verlag. Lect. Notes Math. 1995 (2010).
- 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]
- K. Kime, Simultaneous control of a rod equation and a simple Schrödinger equation. Syst. Control Lett. 24 (1995) 301–306. [CrossRef]
- O.A. Ladyzhenskaya, V.A. Solonnikov and N.N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type. Am. Math. Soc., Providence, RI (1968).
- S. Lenhart and M. Liang, Bilinear optimal control for a wave equation with viscous damping. Houston J. Math. 26 (2000) 575–595. [MathSciNet]
- M. Liang, Bilinear optimal control for a wave equation. Math. Models Methods Appl. Sci. 9 (1999) 45–68. [CrossRef]
- J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag (1971).
- 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]
- A.I. Prilepko, D.G. Orlovsky and I.A. Vasin, Methods for solving inverse problems in mathematical physics. Marcel Dekker Inc., New York (2000).
- R. Rink and R.R. Mohler, Completely controllable bilinear systems. SIAM J. Control 6 (1968) 477–486. [CrossRef] [MathSciNet]
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