Risk-sensitive filtering and smoothing via reference probability methods

IEEE Transactions on Automatic Control

Volumn 42, Issue 11, 1997, Pages 1587-1591

  Dey, Subhrakanti ^a   Moore, John B ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Estimation theory; Optimal filtering; Smoothing

Indexed keywords

DISCRETE TIME CONTROL SYSTEMS; ERROR ANALYSIS; MATHEMATICAL MODELS; NONLINEAR CONTROL SYSTEMS; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; PARAMETER ESTIMATION; PROBABILITY; STATE SPACE METHODS; STOCHASTIC CONTROL SYSTEMS;

FIXED INTERVAL SMOOTHING; REFERENCE PROBABILITY METHODS; RISK SENSITIVE FILTERING;

KALMAN FILTERING;

EID: 0031272804     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.649727     Document Type: Article

References (27)

1. B. D. O. Anderson and J. B. Moore, Optimal Filtering. Englewood Cliffs, NJ: Prentice-Hall, 1979.
2. J. L. Speyer, C. Fan, and R. N. Banavar, "Optimal stochastic estimation with exponential cost criteria," in Proc. 31st Conf. Decision Contr., Dec. 1992, vol. 2, pp. 2293-2298.
3. R. J. Elliott, L. Aggoun, and J. B. Moore, Hidden Markov Models: Estimation and Control, Appl. Math. Series. New York: Springer-Verlag, 1994.
4. I. B. Collings, M. R. James, and J. B. Moore, "An information-state approach to risk-sensitive tracking problems," J. Math. Syst., Estimation, Contr., vol. 6, no. 3, July 1996.
5. P. Whittle, "Risk-sensitive linear/quadratic/Gaussian control," Adv. Appl. Probability 13, pp. 745-777, 1981.
6. _, Risk-Sensitive Optimal Control. New York: Wiley, 1990.
7. A. Bensoussan and J. H. van Schuppen, "Optimal control of partially observable stochastic systems with an exponential-of-integral performance index," SIAM J. Contr. Opt., vol. 23, pp. 599-613, 1985.
8. D. H. Jacobson, "Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic games," IEEE Trans. Automat. Contr., vol. AC-18, pp. 124-131, Apr. 1973.
9. M. R. James, J. S. Baras, and R. J. Elliott, "Risk-sensitive control and dynamic games for partially observed discrete-time systems," IEEE Trans. Automat. Contr., vol. 39, pp. 780-792, 1994.
10. R. J. Elliott, "A general recursive discrete-time filter," J. Appl. Probability, vol. 30, pp. 575-588, 1993.
11. ∞ optimal estimation: The discrete-time case," in Proc. 9th Int. Symp. MTNS, Kobe, Japan, June 1991, pp. 261-267.
12. ∞ estimation," in Proc. Fifth Symp. Dynamic Games, Griementz, Switzerland, June 1992, pp. 504-508.
13. L. Aggoun, A. Bensoussan, R. J. Elliott, and J. B. Moore, "Finite-dimensional quasilinear risk-sensitive control," Syst. Contr. Lett.
14. A. Segall, "Recursive estimation from discrete-time point processes," IEEE Trans. Inform. Theory, vol. IT-22, no. 4, pp. 422-431, 1976.
15. J. B. Moore, R. J. Elliott, and S. Dey, "Risk-sensitive generalizations of minimum variance estimation and control," J. Math. Syst., Estimation Contr., to be published.
16. S. Dey and J. B. Moore, "Risk-sensitive filtering and smoothing via reference probability methods," in Proc. Amer. Contr. Conf., Seattle, June 1995, vol. 1, pp. 129-133.
17. _, "Risk-sensitive filtering and smoothing for hidden Markov models," Syst. Contr. Lett., vol. 25, pp. 361-366, Aug. 1995.
18. O. Zeitouni, "On the reference probability approach to the equations of nonlinear filtering," Stochastics, vol. 19, pp. 133-149, 1986.
19. E. Pardoux, Nonlinear Filtering and Stochastic Control, Lecture Notes in Mathematics, 1981, p. 981.
20. V. Krishnamurthy and S. Dey, "On weak ergodicity of filters for hidden Markov models," to be published.
21. R. K. Boel, J. B. Moore, and S. Dey, "Geometric convergence of filters for hidden Markov models," in Proc. 34th IEEE Conf. Decision Contr., New Orleans, LA, Dec. 1995, pp. 69-74.
22. S. Dey and J. B. Moore, "On finite-dimensional risk-sensitive estimation," in Proc. Int. Symp. Signal Processing Its Appl., Gold Coast, Australia, Aug. 1995, to be published.
23. _, "Finite-dimensional risk-sensitive filters and smoothers for discrete-time nonlinear systems," to be published.
24. J. Levine and G. Pignie, "Exact finite-dimensional filters for a class of nonlinear discrete-time systems," Stochastics, vol. 18, pp. 97-132, 1986.
25. J. B. Moore and J. S. Baras, "Finite-dimensional optimal controllers for nonlinear plants," Syst. Contr. Lett., vol. 26, pp. 223-230, 1995.
26. P. R. Kumar and P. Varaiya, Stochastic Systems. Englewood Cliffs, NJ: Prentice-Hall, 1986.
27. B. D. O. Anderson and I. B. Rhodes, "Smoothing algorithms for nonlinear finite-dimensional systems," Stochastics, vol. 9, pp. 139-165, 1983.