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Information States in Control Theory: From Classical to Quantum

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Mathematical Methods in Systems, Optimization, and Control

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 222))

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Abstract

This paper is concerned with the concept of information state and its use in optimal feedback control of classical and quantum systems. The use of information states for measurement feedback problems is summarized. Generalization to fully quantum coherent feedback control problems is considered.

Mathematics Subject Classification. 93E03, 81Q93.

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References

  1. T. Basar and P. Bernhard. H ∞ -Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach. Birkhäuser, Boston, second edition, 1995.

    Book  Google Scholar 

  2. V.P. Belavkin. On the theory of controlling observable quantum systems. Automation and Remote Control, 44(2):178–188, 1983.

    MathSciNet  MATH  Google Scholar 

  3. V.P. Belavkin. Quantum continual measurements and a posteriori collapse on CCR. Commun. Math. Phys., 146:611–635, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  4. V.P. Belavkin. Quantum stochastic calculus and quantum nonlinear filtering. J. Multivariate Analysis, 42:171–201, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  5. A. Bensoussan and J.H. van Schuppen. Optimal control of partially observable stochastic systems with an exponential-of-integral performance index. SIAM Journal on Control and Optimization, 23:599-613, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  6. L. Bouten, R. van Handel, and M.R. James. An introduction to quantum filtering. SIAM J. Control and Optimization, 46(6):2199–2241, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Carmichael. An Open Systems Approach to Quantum Optics. Springer, Berlin, 1993.

    MATH  Google Scholar 

  8. A.C. Doherty and K. Jacobs. Feedback-control of quantum systems using continuous state-estimation. Phys. Rev. A, 60:2700, 1999.

    Article  Google Scholar 

  9. R.J. Elliott. Stochastic Calculus and Applications. Springer Verlag, New York, 1982.

    Google Scholar 

  10. 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, 31(6):3761–3774, 1985.

    Article  MathSciNet  Google Scholar 

  11. C.W. Gardiner and P. Zoller. Quantum Noise. Springer, Berlin, 2000.

    Google Scholar 

  12. J. Gough and M.R. James. The series product and its application to quantum feedforward and feedback networks. IEEE Trans. Automatic Control, 54(11):2530–2544, 2009.

    Article  MathSciNet  Google Scholar 

  13. J.W. Helton and M.R. James. Extending H ∞ Control to Nonlinear Systems: Control of Nonlinear Systems to Achieve Performance Objectives, volume 1 of Advances in Design and Control. SIAM, Philadelphia, 1999.

    Google Scholar 

  14. R.L. Hudson and K.R. Parthasarathy. Quantum Ito’s formula and stochastic evolutions. Commun. Math. Phys., 93:301–323, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  15. D.H. Jacobson. Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential games. IEEE Transactions on Automatic Control, 18(2):124–131, 1973.

    Article  MATH  Google Scholar 

  16. M.R. James. Risk-sensitive optimal control of quantum systems. Phys. Rev. A, 69:032108, 2004.

    Article  Google Scholar 

  17. M.R. James. A quantum Langevin formulation of risk-sensitive optimal control. J. Optics B: Semiclassical and Quantum,, Special Issue on Quantum Control, 7(10):S198–S207, 2005.

    Google Scholar 

  18. M.R. James and J.S. Baras. Robust H ∞ output feedback control for nonlinear systems. IEEE Transactions on Automatic Control, 40:1007–1017, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  19. M.R. James, J.S. Baras, and R.J. Elliott. Risk-sensitive control and dynamic games for partially observed discrete-time nonlinear systems. IEEE Transactions on Automatic Control, 39:780–792, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  20. M.R. James and J. Gough. Quantum dissipative systems and feedback control design by interconnection. IEEE Trans Auto. Control, 55(8):1806–1821, August 2010.

    Article  MathSciNet  Google Scholar 

  21. M.R. James, H. Nurdin, and I.R. Petersen. H ∞ control of linear quantum systems. IEEE Trans Auto. Control, 53(8):1787–1803, 2008.

    Article  MathSciNet  Google Scholar 

  22. P.R. Kumar and P. Varaiya. Stochastic Systems: Estimation, Identification and Adaptive Control. Prentice-Hall, Englewood Cliffs, NJ, 1986.

    Google Scholar 

  23. H. Mabuchi. Coherent-feedback quantum control with a dynamic compensator. Phys. Rev. A, 78(3):032323, 2008.

    Google Scholar 

  24. H. Nurdin, M.R. James, and A.C. Doherty. Network synthesis of linear dynamical quantum stochastic systems. SIAM J. Control and Optim., 48(4):2686–2718, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  25. H. Nurdin, M.R. James, and I.R. Petersen. Coherent quantum LQG control. Automatica, 45:1837–1846, 2009.

    MathSciNet  MATH  Google Scholar 

  26. K.R. Parthasarathy. An Introduction to Quantum Stochastic Calculus. Birkhäuser, Berlin, 1992.

    Google Scholar 

  27. P. Whittle. Risk-sensitive linear/ quadratic/ Gaussian control. Advances in Applied Probability, 13:764–777, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  28. S.D. Wilson, C. D’Helon, A.C. Doherty, and M.R. James. Quantum risk-sensitive control. In Proc. 45th IEEE Conference on Decision and Control, pages 3132-3137, December 2006.

    Google Scholar 

  29. H.M. Wiseman and G.J. Milburn. Quantum Measurement and Control. Cambridge University Press, Cambridge, UK, 2010.

    Google Scholar 

  30. M. Yanagisawa and H. Kimura. Transfer function approach to quantum controlpart I: Dynamics of quantum feedback systems. IEEE Trans. Automatic Control, (48):2107–2120, 2003.

    Article  MathSciNet  Google Scholar 

  31. M. Yanagisawa and H. Kimura. Transfer function approach to quantum control-part II: Control concepts and applications. IEEE Trans. Automatic Control, (48):2121– 2132, 2003.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. ARC Centre for Quantum Computation and Communication Technology Research School of Engineering, Australian National University, Canberra, ACT, 0200, Australia

    M. R. James

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  1. M. R. James
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Correspondence to M. R. James .

Editor information

Editors and Affiliations

  1. Dept. Mathematics, Weizmann Institute of Science, Rehovot, Israel

    Harry Dym

  2. , Department of Mechanical and, University of California San Diego, Gilman Drive 9500, La Jolla, 92093-0411, California, USA

    Mauricio C. de Oliveira

  3. College of Letters & Science, Dept. Mathematics, University of California, Santa Barbara, Santa Barbara, 93106, California, USA

    Mihai Putinar

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James, M.R. (2012). Information States in Control Theory: From Classical to Quantum. In: Dym, H., de Oliveira, M., Putinar, M. (eds) Mathematical Methods in Systems, Optimization, and Control. Operator Theory: Advances and Applications, vol 222. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0411-0_17

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