Information states in stochastic control and filtering: a lie algebraic theoretic approach

IEEE Transactions on Automatic Control

Volumn 45, Issue 4, 2000, Pages 653-674

  Charalambous, Charalambos D ^a   Elliott, Robert J ^b  

^a UNIVERSITY OF OTTAWA   (Canada)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; NONLINEAR CONTROL SYSTEMS; NONLINEAR FILTERING; OPTIMAL CONTROL SYSTEMS; QUANTUM THEORY; STOCHASTIC CONTROL SYSTEMS;

FINITE DIMENSIONAL; GAUGE TRANSFORMATIONS; INFORMATION STATE; LIE ALGEBRAIC THEORY; MINIMAX; SUFFICIENT STATISTICS;

LINEAR ALGEBRA;

EID: 0034171518     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.847102     Document Type: Article

References (32)

1. E. Wong and B. Hajek, Stochastic Processes in Engineering Systems. New York: Springer-Verlag, 1985.
2. R. Brockett, "Remarks on finite dimensional nonlinear estimation," Analyse des Systems, Asterisque, vol. 75, pp. 47-55, 1980.
3. R. Brockett and J. Clark, "Geometry of the conditional density equation," in Proc. Int. Conf. Analysis and Optimization of Stochastic Systems, Oxford, U.K., 1978.
4. S. Mitter, "On the analogy between mathematical problems of nonlinear filtering and quantum physics," Ricerche di Automatice, vol. 10, no. 2, pp. 163-216, 1979.
5. M. Hazewinkel and J. Willems, "Stochastic systems: The mathematics of filtering and identification and applications," in Proceedings of the NATO Advanced Study Institute: D. Reidel, 1981.
6. L. Tam, W. Wong, and S.-T. Yau, "On a necessary and sufficient condition for finite dimensionality of estimation algebras," SIAM J. Contr. Optimization, vol. 28, no. 1, pp. 173-185, 1990.
7. S. S.-T. Yau, "Finite dimensional filters with nonlinear drift I: A class of filters including both Kalman-Bucy filters and Benes filters," J. Mathematical Systems, Estimation, Contr., vol. 4, no. 2, pp. 181-203, 1994.
8. V. Benes, "Exact finite-dimensional filters for certain diffusions with nonlinear drift," aochastics, vol. 5, pp. 65-92, 1981.
9. S. Marcus, "Algebraic and geometric methods in nonlinear filtering," SIAM J. Contr. Optimization, vol. 26, no. 5, pp. 817-844, 1984.
10. W. Wong, "On a new class of finite dimensional estimation algebras," Syst. Contr. Letters, vol. 9, pp. 79-83, 1987.
11. U. Haussmann and E. Pardoux, "A conditionally almost linear filtering problem with non-Gaussian initial condition," Stochastics, vol. 23, pp. 241-275, 1988.
12. J. Chen, S.-T. Yau, and C.-W. Leung, "Finite-dimensional filters with nonlinear drift IV: Classification of finite-dimensional estimation algebras of maximal rank with state-space dimension 3," SIAM J. Contr. Optimization, vol. 34, no. 1, pp. 179-198, 1996.
13. C. Charalambous and R. Elliott, "New explicit filters and smoothers for diffusions with nonlinear drift and measurements," Syst. Contr. Letters, vol. 33, pp. 89-103, 1998.
14. R. E. Mortensen, "Stochastic optimal control with noisy observations," Int. J. Contr., vol. 4, pp. 455-464, 1966.
15. C. Charalambous, D. Naidu, and K. Moore, "Solvable risk-sensitive control problems with output feedback," in 33rd IEEE Conf. Decision Contr., Lake Buena Vista, FL, Dec. 1994.
16. A. Bensoussan and R. Elliott, "General finite dimensional risk sensitive problems and small noise limits," IEEE Trans. Automat. Contr., vol. 41, pp. 210-215, Feb. 1996.
17. C. Charalambous, "Partially observable nonlinear risk-sensitive control problems: Dynamic programming and verification theorems," IEEE Trans. Automat. Contr., vol. 42, pp. 1130-1138, Aug. 1997.
18. C. Charalambous and R. J. Elliott, "Classes of nonlinear partially observable stochastic optimal control problems with explicit optimal control laws," SIAM J. Contr. Optimization, vol. 36, no. 2, pp. 542-578, 1998.
19. _, "Certain nonlinear stochastic optimal control problems with explicit control laws equivalent to LEQG/LQG problems," IEEE Trans. Automat. Contr., vol. 42, pp. 482-497, Apr. 1997.
20. C. Charalambous and J. Hibey, "Minimum principle for partially observable nonlinear risk-sensitive control problems using measure-valued decompositions," Stochastics and Stochastics Rep., vol. 57, pp. 247-288, 1996.
21. A. Bensoussan, Stochastic Control of Partially Observable Systems Cambridge, U.K.: Cambridge Univ., 1992.
22. _, "Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions," Stochastics, vol. 9, pp. 169-222, 1983.
23. R. S. Liptser and A. N. Shiryayev, Statistics of Random Processes. New York: Springer-Verlag, 1977, vol. 1.
24. V. E. Benes and I. Karatzas, "On the relation of Zakai's and Mortensen's equations," SIAM J. Contr. Optimization, vol. 21, no. 3, pp. 472-489, 1983.
25. S. K. Mitter and A. Moro, Eds., Nonlinear Filtering and Stochastic Control. Berlin, Germany: Springer-Verlag, 1982, vol. 972, Lecture Notes in Mathematics.
26. W. H. Fleming and E. Pardoux, "Optimal control for partially observed diffusions," SIAM J. Contr. Optimization, vol. 20, no. 2, pp. 261-285, 1982.
27. A. Friedman, Stochastic Differential Equations and Applications. New York: Academic, 1975.
28. A. Bensoussan and R. Elliott, "A finite dimensional risk-sensitive control problem," SIAM J. Contr. Optimization, vol. 33, no. 6, pp. 1834-1846, 1995.
29. ∞-norm bound and relations to risk-sensitivity," Syst. Contr. Letters, vol. 11, pp. 167-172, 1988.
30. C. Charalambous, R. J. Elliott, and V. Krishnamurthy, "Conditional moment generating functions for integrals and stochastic integrals," SIAM J. Contr. Optimiz., to be published.
31. P. D. Pra, L. Meneghini, and W. Runggaldier, "Some connections between stochastic control and dynamic games,", Preprint, 1997.
32. C. Charalambous, "The role of informations state and adjoint in relating nonlinear output feedback risk-sensitive control and dynamic games," IEEE Trans. Automat. Contr., vol. 42, pp. 1163-1170, Aug. 1997.