Lyapunov control of bilinear Schrödinger equations

Automatica

Volumn 41, Issue 11, 2005, Pages 1987-1994

  Mirrahimi, Mazyar ^a   Rouchon, Pierre ^a   Turinici, Gabriel ^b,c  

^a PSL RESEARCH UNIVERSITY   (France)

^b INRIA ROCQUENCOURT   (France)

^c UNIVERSITÉ PARIS EST   (France)

Author keywords

Adiabatic invariant; Control Lyapunov function; Quantum systems; Stabilization; Tracking; Trajectory generation

Indexed keywords

ASYMPTOTIC STABILITY; CLOSED LOOP CONTROL SYSTEMS; COMPUTER SIMULATION; LINEAR SYSTEMS; TRAJECTORIES;

ADIABATIC INVARIANCE; ASYMPTOTIC TRACKING; TRAJECTORY TRACKING;

LYAPUNOV METHODS;

EID: 24944551258     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2005.05.018     Document Type: Article

References (35)

1. F. Albertini, and D. D'Alessandro Notions of controllability for bilinear multilevel quantum systems IEEE Transactions on Automatic Control 48 8 2003 1399 1403
2. C. Altafini Controllability of quantum mechanical systems by root space decomposition of su(n) Journal of Mathematical Physics 43 5 2002 2051 2062
3. Beauchard, K., Coron, J.-M., Mirrahimi, M., & Rouchon, P. (2004). Stabilization of a finite dimensional Schrödinger equation. System and Control Letters, submitted for publication.
4. R. Brockett Lie theory and control systems defined on spheres SIAM Journal of Applied Mathematics 25 2 1973 213 225
5. Y. Chen, P. Gross, V. Ramakrishna, H. Rabitz, and K. Mease Competitive tracking of molecular objectives described by quantum mechanics Journal of Chemistry and Physics 102 1995 8001 8010
6. T. Constantinescu, and V. Ramakrishna Parametrizing quantum states and channels Quantum Information Processing 2 2003 221 248
7. A. Elgart, and J.E. Avron Adiabatic theorem without a gap condition Communications in Mathematical Physics 203 1999 445 463
8. Ferrante, A., Pavon, M., & Raccanelli, G. (2002). Control of quantum systems using model-based feedback strategies. In Proceedings of the international symposium MTNS'2002.
9. Gauthier, J. P. (1984). Struture des Systèmes Non- Linéaires. Edition du CNRS.
10. Grivopoulos, S., & Bamieh, B. (2003). Lyapunov-based control of quantum systems. In Proceedings of the 42nd IEEE conference on decision and control.
11. P. Gross, D. Neuhauser, and H. Rabitz Optimal control of unimolecular reactions in the collisional regime Journal of Chemistry and Physics 94 1991 1158 1166
12. P. Gross, H. Singh, H. Rabit, K. Mease, and G.M. Huang Inverse quantum-mechanical control: A means for design and a test of intuition Physical Review A 47 1993 4593
13. V. Jurdjevic, and J.P. Quinn Controllability and stability Journal of Differential Equations 28 1978 381 389
14. T. Kato Perturbation theory for linear operators 1966 Springer Berlin
15. H.K. Khalil Nonlinear systems 1992 MacMillan New York
16. R. Kosloff, S.A. Rice, P. Gaspard, S. Tersigni, and D.J. Tannor Wavepacket dancing: Achieving chemical selectivity by shaping light pulses Chemical Physics 139 1989 201 220
17. Y. Maday, and G. Turinici New formulations of monotonically convergent quantum control algorithms Journal of Chemistry and Physics 118 18 2003
18. A. Martinez Precise exponential estimates in adiabatic theory Journal of Mathematical Physics 35 B 1994
19. Messiah, A. (1962). Quantum mechanics vols. I&II. Amsterdam: North-Holland.
20. Mirrahimi, M., & Rouchon, P. (2004a). Trajectory generation for quantum systems based on lyapounov techniques. In Proceedings of IFAC symposium NOLCOS'2004.
21. Mirrahimi, M., & Rouchon, P. (2004b). Trajectory tracking for quantum systems: A lyapounov approach. In Proceedings of the international symposium MTNS'2004.
22. M. Mirrahimi, G. Turinici, and P. Rouchon Reference trajectory tracking for locally designed coherent quantum controls Journal of Physical Chemistry A 109 2005 2631 2637
23. M.Q. Phan, and H. Rabitz Learning control of quantum-mechanical systems by laboratory identification of effective input-output maps Chemical Physics 217 1997 389 400
24. M.Q. Phan, and H. Rabitz A self-guided algorithm for learning control of quantum-mechanical systems Journal of Chemistry and Physics 110 1999 34 41
25. W. Rabitz, and H. anf Zhu Quantum control design via adaptive tracking Journal of Chemistry and Physics 119 7 2003
26. V. Ramakrishna, R.J. Ober, K.L. Flores, and H. Rabitz Control of a coupled two-spin system without hard pulses Physical Review A 65 2002 063405-1-9
27. V. Ramakrishna, M. Salapaka, M. Dahleh, and H. Rabitz Controllability of molecular systems Physical Review A 51 2 1995 960 966
28. S. Shi, A. Woody, and H. Rabitz Optimal control of selective vibrational excitation in harmonic linear chain molecules Journal of Chemistry and Physics 88 11 1988 6870 6883
29. M. Sugawara General formulation of locally designed coherent control theory for quantum systems Journal of Chemistry and Physics 118 15 2003 6784 6800
30. H.J. Sussmann, and V. Jurdjevic Controllability of nonlinear systems Journal Differential Equations 12 1972 95 116
31. S.H. Tersigni, P. Gaspard, and A. Rice On using shaped light pulses to control the selectivity of product formation in a chemical reaction: An application to a multiple level system Journal of Chemistry and Physics 93 3 1990 1670 1680
32. G. Turinici, and H. Rabitz Quantum wavefunction controllability Chemical Physics 267 2001 1 9
33. G. Turinici, and H. Rabitz Wavefunction controllability in quantum systems Journal of Physics A 36 2003 2565 2576
34. Vaidya, U., D'Alessandro, D., & Mezic, I. (2003). Control of heisenberg spin systems; lie algebraic decompositions and action-angle variables. In Proceedings of the 42nd IEEE conference on decision and control.
35. Vettori, P. (2002). On the convergence of a feedback control strategy for multilevel quantum systems. In Proceedings of the international symposium MTNS'2002.