Hamilton-Jacobi-Bellman equations for quantum optimal feedback control

Journal of Optics B: Quantum and Semiclassical Optics

Volumn 7, Issue 10, 2005, Pages

  Gough, J ^a   Belavkin, V P ^b   Smolyanov, O G ^c  

^a NOTTINGHAM TRENT UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^c MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Optimal quantum control; Quantum Bellman principle; Quantum diffusion filtering; Quantum dynamical programming; Quantum feedback control; Quantum Hamilton Jacobi equation

Indexed keywords

CONTINUUM MECHANICS; FILTRATION; HAMILTONIANS; QUANTUM OPTICS; SEPARATION;

OPTIMAL QUANTUM CONTROL; QUANTUM BELLMAN PRINCIPLE; QUANTUM DIFFUSION FILTERING; QUANTUM DYNAMICAL PROGRAMMING; QUANTUM FEEDBACK CONTROL; QUANTUM-HAMILTONIAN-JACOBI EQUATION;

FEEDBACK CONTROL;

EID: 25644444468     PISSN: 14644266     EISSN: None     Source Type: Journal    
DOI: 10.1088/1464-4266/7/10/006     Document Type: Review

References (34)

1. Armen M, Au J, Stockton J, Doherty A and Mabuchi H 2002 Adaptive homodyne measurement of optical phase Phys. Rev. A 89 133602
2. Belavkin V P 1978 Optimal quantum filtration of Markovian signals Probl. Control Inf. Theory 7 345-60
3. Belavkin V P 1979 Optimal measurement and control in quantum dynamical systems Preprint No. 411 (Inst. of Phys., Nicolaus Copernicus University, Torun)
4. Belavkin V P 1980 Quantum filtering of Markov signals with Wight quantum noise Radiotech. Electron. 25 1445-53
5. Belavkin V P 1994 Quantum Communications and Measurement ed V P Belavkin et al (New York: Plenum) pp 381-92 (Engl. Transl.)
6. Belavkin V P 1983 Theory of the control of observable quantum systems Autom. Remote Control 44 178-88
7. Belavkin V P 1987 Nondemolition measurement and control in quantum dynamical systems Information Complexity and Control in Quantum Physics (Udine, 1985) (CISM Courses and Lectures vol 294) (Vienna: Springer) pp 311-29
8. Belavkin V P 1988 Nondemolition measurements, nonlinear filtering and dynamical programming of quantum stochastic processes Modelling and Control of Systems (Lecture Notes in Control and Information Sciences vol 121) ed A Blaquiere (Berlin: Springer) pp 381-92
9. Belavkin V P 1989 A new wave equation for continuous nondemolition measurement Phys. Lett. A 140 355-8
10. Belavkin V P 1990 Stochastic posterior equations for quantum nonlinear filtering Probability Theory and Mathematical Statistics vol 1 ed B Grigelionis (Vilnius: VSP/Mokslas) pp 91-109
11. Belavkin V P 1992 Quantum stochastic calculus and quantum nonlinear filtering J. Multivariate Anal. 42 171-201
12. Belavkin V P 1992 Quantum continual measurements and a posteriori collapse on CCR Commun. Math. Phys. 146 611-35
13. Belavkin V P 1999 Measurement, filtering and control in quantum open dynamical systems Rep. Math. Phys. 43 405-25
14. Bellman R 1957 Dynamic Programming (Princeton, NJ: Princeton University Press)
15. Bismut J M 1981 Mechanique Aléatoire Lecture Notes in Mathematics vol 866 (Berlin: Springer)
16. Bouten L, Edwards S and Belavkin V P 2004 Bellman equations for optimal feedback control of qubit states Preprint quant-ph/0407192v1
17. Bouten L, Guţǎ M and Maassen H 2004 Stochastic Schrödinger equations J. Phys. A: Math. Gen. 37 3189-209
18. Davis M H A 1977 Linear Estimation and Stochastic Control (London: Chapman and Hall)
19. Da Prato G and Zabczyk J 1992 Stochastic Equations in Infinite Dimensions (Encyclopedia of Mathematics and its Applications) (Cambridge: Cambridge University Press)
20. Doherty A, Habib S, Jacobs K, Mabuchi H and Tan S 2000 Quantum feedback and classical control theory Phys. Rev. A 62 012105
21. Gardiner C W 2004 Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Berlin: Springer)
22. Geremia J, Stockton J, Doherty A and Mabuchi H 2003 Quantum Kalman filtering and the Heisenberg limit in atomic magnetometry Phys. Rev. Lett. 91 250801
23. Gough J and Sobolev A 2004 Stochastic Schrödinger equations as limit of discrete filtering Open Syst. Inf. Dyn. 11 235-55
24. Gough J and Sobolev A 2004 Continuous measurement of canonical observables and limit stochastic Schrödinger equations Phys. Rev. A 69 032107
25. van Handel R, Stockton J and Mabuchi H 2004 Feedback control of quantum state reduction Preprint quant-ph/0402136
26. James M R 2004 Risk-sensitive optimal control of quantum systems Phys. Rev. A 69 032108
27. Parthasarathy K R 1992 An Introduction to Quantum Stochastic Calculus (Berlin: Birkhäuser)
28. Pontryagin L S, Boltyanskii V G, Gamkrelidze R V and Mishchenko E F 1962 The Mathematical Theory of Optimal Processes (New York: Wiley)
29. Scott A J and Milburn G J 2001 Quantum nonlinear dynamics of continuously measured systems Phys. Rev. A 63 042101 (Preprint quant-ph/0008108)
30. Smolyanov O G and Truman A 1993 Schrödinger-Belavkin equations and associated Kolmogorov and Lindblad equations Theor. Math. Phys. 120 973-84
31. Stratonovich R L 1966 A new representation of stochastic integrals and equations SIAM J. Control 4 362-71
32. Truman A and Zhao H Z 1996 The stochastic Hamilton-Jacobi equation, stochastic heat equations and Schrödinger equations Stochastic Analysis and Applications ed D Elworthy, I M Davies and A Truman (Singapore: World Scientific) pp 441-64
33. Wiseman M and Milburn G J 1993 Quantum theory of optical feedback via homodyne detection Phys. Rev. Lett. 70 548-51
34. Wong E and Zakai M 1965 On the relationship between ordinary and stochastic differential equations Int. J. Eng. Sci. 3 213-29