A duality relationship for regular conditional relative entropy

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 16, Issue , 2005, Pages 248-253

  Xie, Li ^a   Ugrinovskii, Valery A ^a   Petersen, Ian R ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Duality relationship; Radon nikodym derivative; Regular conditional probability measure; Regular conditional relative entropy; Sub sigma algebra

Indexed keywords

ALGEBRA; FREE ENERGY; HIDDEN MARKOV MODELS;

CONDITIONAL PROBABILITIES; DUALITY RELATIONS; DUALITY RELATIONSHIP; FINITE ALPHABET; PROBABILITY MEASURES; RADON-NIKODYM DERIVATIVE; RELATIVE ENTROPY; ROBUST STATE ESTIMATION;

ENTROPY;

EID: 79960714165     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20050703-6-cz-1902.00394     Document Type: Conference Paper

References (18)

1. Boel, R.K., M.R. James and I.R. Petersen (2002). Robustness and risk-sensitive filtering. IEEE Transactions on Automatic Control 47(3), 451-461.
2. Charalambous, C.D., F. Rezaei and S.D. Djouadi (2003). Characterization of the optimal disturbance attenuation for nonlinear stochastic uncertain systems. In: Proceedings of the 42nd IEEE Conference on Decision & Control.
3. Chow, Y.S. and H. Teicher (1988). Probability Theory, independence, interchangeability, martingales. 2nd ed., Springer Verlag.
4. Dai Pra, P., L. Meneghini and W.J. Runggaldier (1996). Connections between stochastic control and dynamic games. Mathematics of Control, Signals, and Systems 9(4), 303-326.
5. Dellacherie, C. and P.A. Meyer (1982). Probability and Potentials B. North-Holland. Amsterdam. Translated by I.P. Wilson.
6. Deuschel, J.-D. and D.W. Stroock (1989). Large Deviations. Academic Press. San Diego.
7. Dey, S. and J.B. Moore (1995). Risk-sensitive filtering and smoothing for hidden Markov models. Systems & Control Letters 25, 361- 366.
8. Dupuis, P. and E. Ellis (1997). A Week Convergence Approach to the Theory of Large Deviations. Wiley, New York.
9. Elliott, R.J., L. Aggoun and J.B. Moore (1994). Hidden Markov Models: Estimation and Control. Springer-Verlag. New York.
10. Ephraim, Y.E. and N. Merhav (2002). Hidden Markov processes. IEEE Transactions on Information Theory 48(6), 1518-1569.
11. Kallenberg, O. (1997). Foundations of Modern Probability. Springer-Verlag.
12. Mitter, S.K. and N.J. Newton (2003). A variational approach to nonlinear estimation. SIAM Journal on Control and Optimization 42(5), 1813-1833.
13. Petersen, I.R., M.R. James and P. Dupuis (2000). Minimax optimal control of stochastic uncertain systems with relative entropy constraints. IEEE Transactions on Automatic Control 45(3), 398-412.
14. Shiryayev, A.N. (1984). Probability. Springer-Verlag. Translated by R.P. Boas.
15. Stroock, D.W. and S.R.S. Varadhan (1979). Multidimensional Diffusion Processes. Spring-Verlag. New York.
16. Ugrinovskii, V.A. and I.R. Petersen (1999). Finite horizon minimax optimal control of stochastic partially observed time varying uncertain systems. Mathematics of Control, Signals and Systems 12, 1-23.
17. Wu, L.M. (1997). An introduction to large deviations. In: Several Topics in Stochastic Analysis (J.A. Yan, S.G. Peng, S.Z. Fang and L.M. Wu, Eds.). Press of Sciences of China. pp. 225-336. in Chinese, Beijing.
18. Xie, L., V.A. Ugrinovskii and I.R. Petersen (2004). Finite horizon robust state estimation of uncertain finite-alphabet hidden Markov models with regular conditional relative entropy constraints. Accepted by the 43rd IEEE Conference on Decision & Control, 2004.