Quantum dissipative systems and feedback control design by interconnection

IEEE Transactions on Automatic Control

Volumn 55, Issue 8, 2010, Pages 1806-1821

  James, Matthew R ^a   Gough, John E ^b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b ABERYSTWYTH UNIVERSITY   (United Kingdom)

Author keywords

Control by interconnection; damping; dissipation; quantum feedback control; quantum feedback networks; quantum noise; regulation; robustness; stabilization

Indexed keywords

ANALYSIS AND DESIGN; BOUNDED REAL LEMMA; CONTROL BY INTERCONNECTION; CONTROL DESIGN; DISSIPATIVE QUANTUM SYSTEMS; DISSIPATIVE SYSTEMS; EXOSYSTEMS; EXTERNAL SYSTEMS; FEEDBACK NETWORKS; NETWORK MODELS; OPEN QUANTUM SYSTEMS; POSITIVE REAL; QUANTUM FEEDBACK; QUANTUM FEEDBACK CONTROL; QUANTUM FEEDBACK NETWORKS; QUANTUM PHYSICS; STANDARD PROBLEMS;

DAMPING; DESIGN; ENERGY DISSIPATION; FEEDBACK CONTROL; QUANTUM ELECTRONICS; QUANTUM NOISE; QUANTUM OPTICS; ROBUST CONTROL; STABILIZATION;

ROBUSTNESS (CONTROL SYSTEMS);

EID: 77955390600     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2046067     Document Type: Article

References (49)

1. B. Anderson and S. Vongpanitlerd, Network Analysis and Synthesis. Englewood Cliffs, NJ: Prentice-Hall, 1973.
2. M. Armen, K. Au, J. Stockton, A. Doherty, and H. Mabuchi, "Adaptive homodyne measurement of optical phase," Phys. Rev. A, vol.89, no.13, p. 133602, 2002.
3. G. Auletta, M. Fortunato, and G. Parisi, Quantum Mech.. Cambridge, U.K.: Cambridge Univ. Press, 2009.
4. V. Belavkin, "On the theory of controlling observable quantum systems," Autom. Remote Control, vol.44, no.2, pp. 178-188, 1983.
5. L. Bouten, R. Van Handel, and M. R. James, "An introduction to quantum filtering," SIAM J. Control Optim., vol.46, no.6, pp. 2199-2241, 2007.
6. H. Carmichael, An Open Systems Approach to Quantum Optics. Berlin, Germany: Springer, 1993.
7. H. J. Carmichael, "Quantum trajectory theory for cascaded open systems," Phys. Rev. Lett., vol.70, no.15, pp. 2273-2276, 1993.
8. E. Davies, Quantum Theory of Open Systems. New York: Academic Press, 1976.
9. C. D'Helon and M. R. James, "Stability, gain, and robustness in quantum feedback networks," Phys. Rev. A., vol.73, p. 053803, 2006.
10. A. C. Doherty and K. Jacobs, "Feedback-control of quantum systems using continuous state-estimation," Phys. Rev. A, vol.60, p. 2700, 1999.
11. C. W. Gardiner, "Driving a quantum system with the output field from another driven quantum system," Phys. Rev. Lett., vol.70, no.15, pp. 2269-2272, 1993.
12. C. W. Gardiner and M. J. Collett, "Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation," Phys. Rev. A, vol.31, no.6, pp. 3761-3774, 1985.
13. C. W. Gardiner and P. Zoller, Quantum Noise. Berlin, Germany: Springer, 2000.
14. J. Gough and M. R. James, "Quantum feedback networks: Hamiltonian formulation," Commun. Math. Phys., vol.287, pp. 1109-1132, 2009.
15. J. Gough and M. R. James, "The series product and its application to quantum feedforward and feedback networks," IEEE Trans. Autom. Control, vol.54, no.11, pp. 2530-2544, Nov. 2009.
16. M. Green and D. J. N. Limebeer, Linear Robust Cotrol. Englewood Cliffs, NJ: Prentice-Hall, 1995.
17. D. Hill and P. Moylan, "The stability of nonlinear dissipative systems," IEEE Trans. Autom. Control, vol.AC-21, no.5, pp. 708-711, Oct. 1976.
18. D. Hill and P. Moylan, "Dissipative dynamical systems: Basic inputoutput and state properties," J. Franklin Inst., vol.309, pp. 327-357, 1980.
19. R. L. Hudson and K. R. Parthasarathy, "Quantum Ito's formula and stochastic evolutions," Commun. Math. Phys., vol.93, pp. 301-323, 1984.
20. M. R. James, H. Nurdin, and I. R. Petersen, " H∞ control of linear quantum systems," IEEE Trans. Autom. Control, vol.53, no.8, pp. 1787-1803, Jul. 2008.
21. G. Lindblad, "On the generators of quantum dynamical semigroups," Commun. Math. Phys., vol.48, pp. 119-130, 1976.
22. S. Lloyd, "Coherent quantum feedback," Phys. Rev. A, vol.62, p. 022108, 2000.
23. H. Mabuchi, "Coherent-Feedback Quantum Control With a Dynamic Compensator," in arXiv:0803.2007, 2008.
24. E. Merzbacher, Quantum Mechanics, 3rd ed. NewYork:Wiley, 1998.
25. P. J. Moylan, "Implications of passivity in a class of nonlinear systems," IEEE Trans. Autom. Control, vol.AC-19, no.4, pp. 373-381, 1974.
26. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information. Cambridge, U.K.: Cambridge Univ. Press, 2000.
27. H. Nurdin, M. R. James, and A. C. Doherty, "Network synthesis of linear dynamical quantum stochastic systems," SIAM J. Control Optim., vol.48, no.4, pp. 2686-2718, 2009.
28. H. Nurdin, M. R. James, and I. R. Petersen, "Coherent quantum LQG control," Automatica, vol.45, pp. 1837-1846, 2009.
29. R. Ortega and M. W. Spong, "Adaptive motion control of rigid robots: A tutorial," Automatica, vol.25, no.6, pp. 877-888, 1989.
30. R. Ortega, A. J. van der Schaft, I. Mareels, and B. Maschke, "Putting energy back in control," IEEE Control Syst. Mag., vol.21, pp. 18-32, Apr. 2001.
31. R. Ortega, A. J. van der Schaft, B. Maschke, and G. Escobar, "Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems," Automatica, vol.38, pp. 585-596, 2002.
32. K. R. Parthasarathy, An Introduction to Quantum Stochastic Calculus. Berlin, Germany: Birkhauser, 1992.
33. L. K. Thomsen and H. M. Wiseman, "Atom-laser coherence and its control via feedback," Phys. Rev. A, vol.65, p. 063607, 2002.
34. H. L. Trentelman and J. C. Willems, " H∞ control in a behavioral context: The full information case," IEEE Trans. Autom. Control, vol.44, no.3, pp. 521-536, Mar. 1999.
35. 2 -Gain and Passivity Techniques in Nonlinear Control. New York: Springer Verlag, 1996.
36. R. van Handel, J. Stockton, and H. Mabuchi, "Feedback control of quantum state reduction," IEEE Trans. Autom. Control, vol.50, no.6, pp. 768-780, Jun. 2005.
37. J. C. Willems, "Dissipative dynamical systems-Part I: General theory," Archive Rat. Mech. Anal., vol.45, pp. 321-351, 1972.
38. J. C. Willems, "On interconnections, control, and feedback," IEEE Trans. Autom. Control, vol.42, no.3, pp. 326-339, Mar. 1997.
39. J. C.Willems, "Open dynamical systems and their control," Documenta Mathematica, vol.ICM(III), pp. 697-706, 1998.
40. J. C.Willems, "Control as interconnection," in Feedback Control, Nonlinear Systems and Complexity. New York: Springer, 2003.
41. J. C. Willems and H. L. Trentelman, "Synthesis of dissipative systems using quadratic differential forms: Part I," IEEE Trans. Autom. Control, vol.47, no.1, pp. 53-69, Jan. 2002.
42. H.Wiseman, "Quantum theory of continuous feedback," Phys. Rev. A, vol.49, no.3, pp. 2133-2150, 1994.
43. H. M. Wiseman and G. J. Milburn, "All-optical versus electro-optical quantum-limited feedback," Phys. Rev. A, vol.49, no.5, pp. 4110-4125, 1994.
44. W. Wiseman and G. Milburn, Quantum Measurement and Control. Cambridge, U.K.: Cambridge Univ. Press, 2010.
45. M. Yanagisawa and H. Kimura, "Transfer function approach to quantum control-part I: Dynamics of quantum feedback systems," IEEE Trans. Autom. Control, vol.48, no.12, pp. 2107-2120, Dec. 2003.
46. M. Yanagisawa and H. Kimura, "Transfer function approach to quantum control-part II: Control concepts and applications," IEEE Trans. Autom. Control, vol.48, no.12, pp. 2121-2132, Dec. 2003.
47. B. Yurke and J. S. Denker, "Quantum network theory," Phys. Rev. A, vol.29, no.3, pp. 1419-1437, 1984.
48. G. Zames, "On the input-output stability of time-varying nonlinear feedback systems Part I: Conditions derived using concepts of loop gain, conicity, and positivity," IEEE Trans. Autom. Control, vol.AC-11, no.2, pp. 228-238, 1966.
49. K. Zhou, J. Doyle, and K. Glover, Robust and Optimal Control. Englewood Cliffs, NJ: Prentice Hall, 1996.