Analysis of effectiveness of lyapunov control for non-generic quantum states

IEEE Transactions on Automatic Control

Volumn 55, Issue 6, 2010, Pages 1406-1411

  Wang, Xiaoting ^a   Schirmer, Sophie G ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Center manifolds; LaSalle invariance principle; Lyapunov control; Quantum systems

Indexed keywords

CENTER MANIFOLD; GLOBAL ASYMPTOTIC STABILITY; LASALLE INVARIANCE PRINCIPLE; LYAPUNOV CONTROL; LYAPUNOV-BASED CONTROL; NONSTATIONARY; QUANTUM STATE; QUANTUM SYSTEM; STATIONARY TARGETS; TARGET STATE; TRAJECTORY-TRACKING PROBLEMS;

ASYMPTOTIC STABILITY; DYNAMICAL SYSTEMS; QUANTUM ELECTRONICS; QUANTUM OPTICS; SWITCHING SYSTEMS;

DESIGN;

EID: 77953087686     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2042760     Document Type: Article

References (14)

1. P. Vettori, "On the convergence of a feedback control strategy for multilevel quantum systems," in Proc. MTNS, 2002, p. 21350.
2. A. Ferrante, M. Pavon, and G. Raccanelli, "Driving the propagator of a spin system: a feedback approach," in Proc. 41st IEEE CDC, 2002, pp. 46-50.
3. S. Grivopoulos and B. Bamieh, "Lyapunov-based control of quantum systems," in Proc. 42nd IEEE CDC, 2003, pp. 431-438.
4. M. Mirrahimi and P. Rouchon, "Trajectory generation for quantum systems based on Lyapunov techniques," in Proc. NOLCOS, 2004, p. 291.
5. M. Mirrahimi and P. Rouchon, "Trajectory tracking for quantum systems: A Lyapunov approach," in Proc. MTNS, 2004, [CD ROM].
6. M. Mirrahimi, P. Rouchon, and G. Turinici, "Lyapunov control of bilinear Schrodinger equations," Automatica, vol.41, pp. 1987-1994, 2005.
7. K. Beauchard, J.-M. Coron, M. Mirrahimi, and P. Rouchon, "Implicit Lyapunov control of finite dimensional Schrodinger equations," Syst. Control Lett., vol.56, pp. 388-395, 2007.
8. M. Mirrahimi and R. Van Handel, "Stabilizing feedback controls for quantum systems," SIAM J. Control Optim., vol.46, pp. 445-467, 2007.
9. C. Altafini, "Feedback control of spin systems," Quantum Inform. Processing, vol.6, pp. 9-36, 2007.
10. C. Altafini, "Feedback stabilization of quantum ensembles: A global convergence analysis on complex flag manifolds," IEEE Trans. Autom. Control, vol.52, no.11, pp. 2019-2028, Nov. 2007.
11. D. D'Alessandro, Introduction to Quantum Control and Dynamics. Orlando, FL: CRC Press, 2007.
12. S. G. Schirmer and X. Wang, "Analysis of Lyapunov method for control of quantum states," IEEE Trans. Autom. Control, to be published.
13. J. LaSalle and S. Lefschetz, Stability by Liapunov's Direct Method with Applications. New York: Academic Press, 1961.
14. R. Wu, H. Rabitz, and M. Hsieh, "Characterization of the critical submanifolds in the quantum ensemble control landscapes," J. Phys. A, vol.41, p. 015006, 2008.