Quantum LQG control with quantum mechanical controllers

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 17, Issue 1 PART 1, 2008, Pages

  Nurdin, Hendra Ishwara ^a   James, Matthew R ^a   Petersen, Ian Richard ^a  

^a NONE

Author keywords

Controller constraints and structure; Linear systems; LMIs

Indexed keywords

ALTERNATING PROJECTIONS; CLASSICAL CONTROLLERS; CONTROLLER CONSTRAINTS AND STRUCTURE; CONTROLLER DESIGNS; DEGREES OF FREEDOM; LINEAR CONSTRAINTS; LINEAR STOCHASTIC SYSTEM; LMIS; LQG CONTROL; NON-LINEAR; NUMERICAL PROCEDURES; NUMERICAL SOLUTION; OPTIMAL CONTROL PROBLEM; PHYSICAL REALIZABILITY; PLANT OUTPUT; PROBLEM-BASED; QUANTUM MECHANICAL; QUANTUM SYSTEM;

LINEAR CONTROL SYSTEMS; NONLINEAR CONTROL SYSTEMS; PROBLEM SOLVING; QUANTUM ELECTRONICS; QUANTUM OPTICS; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC SYSTEMS;

CONTROLLERS;

EID: 79961017899     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20080706-5-KR-1001.0895     Document Type: Conference Paper

References (25)

1. Advanced Optimization Lab, McMaster University . Se- DuMi v1.1R3. URL http://sedumi.mcmaster.ca/. October 2006.
2. M.A. Armen, K.J. Au, J.K. Stockton, A.C. Doherty, and H. Mabuchi. Adaptive homodyne measurement of optical phase. Phys. Rev. A, 89(13):133602, 2002.
3. V.P. Belavkin. On the theory of controlling observable quantum systems. Automation and Remote Control, 44 (2):178 188, 1983.
4. V.P. Belavkin. Continuous non-demolition observation, quantum filtering and optimal estimation. In Quantum Aspects of Optical Communication, volume 45 of Lecture notes in Physics, pages 131-145. Springer, Berlin, 1991.
5. L. Bouten, R. van Handel, and M. R. James. An introduction to quantum filtering. SIAM J. Control Optim., 46 (6):2199-2241, 2007.
6. A.C. Doherty and K. Jacobs. Feedback-control of quantum systems using continuous state-estimation. Phys. Rev. A, 60:2700, 1999. quant-ph/9812004.
7. S. C. Edwards and V. P. Belavkin. Optimal quantum feedback control via quantum dynamic programming. quant-ph/0506018, University of Nottingham, 2005.
8. C.W. Gardiner and P. Zoller. Quantum Noise. Springer, Berlin, 2000.
9. J.M Geremia, J.K. Stockton, and H. Mabuchi. Real-time quantum feedback control of atomic spin-squeezing. Science, 304:270-273, April 2004.
10. D. Henrion and J. B. Lasserre. Convergent relaxations of polynomial matrix inequalities and static output feedback. IEEE Trans. Automat. Contr., 51(2):192-202, 2006.
11. C.W. J. Hol and C. Scherer. Sum of squares relaxations for polynomial semidefinite programming. In Proc. 16th International Symp. Mathemarical Theory and Networks (MTNS) 2004 (Leuven, Belgium, July 5-9, 2004). 2004.
12. R. L. Hudson and K. R. Parthasarathy. Quantum Ito's formula and stochastic evolution. Commun. Math. Phys., 93:301-323, 1984.
13. M. R. James, H. I. Nurdin, and I. R. Petersen. H1 control of linear quantum stochastic systems. URL http://arxiv.org/pdf/quant-ph/0703150 (pre-print). to be published (accepted 24-9-2007) in IEEE Transactions on Automatic Control, arXiv eprint: quant-ph/0703150, 2007.
14. E. Knill, R. Laflamme, and G.J. Milburn. A scheme for efficient quantum computation with linear optics. Nature, 409:46-52, 2001. (Pubitemid 32098618)
15. M. Kojima. Sums of squares relaxations of polynomial semidefinite programs. Technical Report B-397, Dept. Math. Comp. Sci., Tokyo Institute of Technology, Tokyo, Japan, 2003.
16. J. B. Lasserre. Global optimization with polynomials and the problem of moments. SIAM J. Optimization, 11(3): 796-817, 2001.
17. J. Lofberg. Yalmip : A toolbox for modeling and optimization in MATLAB. In Proceedings of the CACSD Conference, Taipei, Taiwan, 2004. URL http://control.ee.ethz.ch/~joloef/yalmip.php.
18. M.A. Nielsen and I.L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, 2000.
19. H. I. Nurdin, M. R. James, and I. R. Petersen. Coherent quantum LQG control. submitted for journal publication, arXiv eprint: arXiv:0711.2551, November 2007.
20. R. Orsi. LMIRank: Software for rank constrained LMI problems. URL http://rsise.anu.edu.au/~robert/lmirank/. 2005.
21. R. Orsi, U. Helmke, and J. B. Moore. A Newtonlike method for solving rank constrained linear matrix inequalities. Automatica J. IFAC, 42(11):1875-1882, 2006. Extended version available at R. Orsi's homepage.
22. K.R. Parthasarathy. An Introduction to Quantum Stochastic Calculus. Birkhauser, Berlin, 1992.
23. C. Scherer, P. Gahinet, and M. Chilali. Multiobjective output-feedback control via LMI optimization. IEEE Trans. Automat. Contr., 42(7):896-911, 1997.
24. A.J. Shaiju, I.R. Petersen, and M.R. James. Guaranteed cost LQG control of uncertain linear stochastic quantum systems. In Proceedings of the 2007 American Control Conference, New York, July 2007.
25. N. Z. Shor. Dual quadratic estimates in polynomial and boolean programming. Ann. Oper. Res., 25:163-168, 1990.