Implicit Lyapunov control of finite dimensional Schrödinger equations

Systems and Control Letters

Volumn 56, Issue 5, 2007, Pages 388-395

  Beauchard, Karine ^a   Coron, Jean Michel ^b   Mirrahimi, Mazyar ^c   Rouchon, Pierre ^c  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b UNIVERSITÉ PARIS SACLAY   (France)

^c PSL RESEARCH UNIVERSITY   (France)

Author keywords

Lyapunov; Quantum system

Indexed keywords

COMPUTER SIMULATION; INVARIANCE; QUANTUM THEORY; SCHRODINGER EQUATION; THEOREM PROVING;

CLOSED-LOOP SIMULATIONS; FEEDBACK LAWS; QUANTUM SYSTEM;

LYAPUNOV FUNCTIONS;

EID: 33947213375     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2006.10.024     Document Type: Article

References (27)

1. Albertini F., and D'Alessandro D. Notions of controllability for bilinear multilevel quantum systems. IEEE Trans. Automat. Control 48 8 (2003) 1399-1403
2. Altafini C. Controllability of quantum mechanical systems by root space decomposition of su(n). J. Math. Phys. 43 5 (2002) 2051-2062
3. C. Altafini, F. Ticozzi, Almost global stochastic feedback stabilization of conditional quantum dynamics, Preprint, 2005.
4. Beauchard K. Local controllability of a 1-D Schrödinger equation. J. Math. Pures Appl. 84 (2005) 851-956
5. Beauchard K., and Coron J.M. Controllability of a quantum particle in a moving potential well. J. Funct. Anal. 232 (2006) 328-389
6. Chen Y., Gross P., Ramakrishna V., Rabitz H., and Mease K. Competitive tracking of molecular objectives described by quantum mechanics. J. Chem. Phys. 102 (1995) 8001-8010
7. Coron J.M. On the null asymptotic stabilization of the two-dimensional incompressible Euler equations in a simply connected domain. SIAM J. Control Optim. 37 (1999) 1874-1896
8. Geremia J.M., and Rabitz H. Optimal hamiltonian identification: the synthesis of quantum optimal control and quantum inversion. J. Chem. Phys. 118 12 (2003) 5369-5382
9. Van Handel R., Stockton J.K., and Mabuchi H. Feedback control of quantum state reduction. IEEE Trans. Automat. Control 50 (2005) 768-780
10. S. Haroche, Contrôle de la décohérence: théorie et expériences, Notes de cours, Collège de France 〈http://www.lkb.ens.fr/recherche/qedcav/college/college.html〉, 2004.
11. Kato T. Perturbation Theory for Linear Operators (1966), Springer, Berlin
12. Khalil H.K. Nonlinear Systems (1992), MacMillan, New York
13. Li B., Turinici G., Ramakrishna V., and Rabitz H. Optimal dynamic discrimination of similar molecules through quantum learning control. J. Phys. Chem. B. 106 33 (2002) 8125-8131
14. Lu Z.-M., and Rabitz H. Unified formulation for control and inversion of molecular dynamics. J. Phys. Chem. 99 (1995) 13731-13735
15. Mabuchi H., and Khaneja N. Principles and applications of control in quantum systems. Internat. J. Robust Nonlinear Control 15 (2005) 647-667
16. Maday Y., and Turinici G. New formulations of monotonically convergent quantum control algorithms. J. Chem. Phys. 118 18 (2003)
17. M. Mirrahimi, R. Van Handel, Stabilizing feedback controls for quantum systems, SIAM J. Cont. Opt., to appear, http://arxiv.org/abs/math-ph/0510066.
18. Mirrahimi M., Rouchon P., and Turinici G. Lyapunov control of bilinear Schrödinger equations. Automatica 41 (2005) 1987-1994
19. Mirrahimi M., Turinici G., and Rouchon P. Reference trajectory tracking for locally designed coherent quantum controls. J. Phys. Chem. A 109 (2005) 2631-2637
20. Rabitz H., and Zhu W. Quantum control design via adaptive tracking. J. Chem. Phys. 119 7 (2003)
21. Ramakrishna V., Salapaka M., Dahleh M., and Rabitz H. Controllability of molecular systems. Phys. Rev. A 51 2 (1995) 960-966
22. P. Rouchon, Control of a quantum particle in a moving potential well, in: IFAC Second Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, April 2003.
23. Shi S., Woody A., and Rabitz H. Optimal control of selective vibrational excitation in harmonic linear chain molecules. J. Chem. Phys. 88 11 (1988) 6870-6883
24. Sugawara M. General formulation of locally designed coherent control theory for quantum systems. J. Chem. Phys. 118 15 (2003) 6784-6800
25. Sussmann H.J., and Jurdjevic V. Controllability of nonlinear systems. J. Differential Equations 12 (1972) 95-116
26. Turinici G., and Rabitz H. Quantum wavefunction controllability. Chem. Phys. 267 (2001) 1-9
27. Turinici G., and Rabitz H. Wavefunction controllability in quantum systems. J. Phys. A 36 (2003) 2565-2576