Stochastic uncertain systems subject to relative entropy constraints: Induced norms and monotonicity properties of minimax games

IEEE Transactions on Automatic Control

Volumn 52, Issue 4, 2007, Pages 647-663

  Charalambous, Charalambos D ^a,b   Rezaei, Farzad ^a  

^a UNIVERSITY OF CYPRUS   (Cyprus)

^b UNIVERSITY OF OTTAWA   (Canada)

Author keywords

Duality properties; Large deviations; Minimax games; Relative entropy; Uncertain stochastic systems

Indexed keywords

CONSTRAINT THEORY; CONTINUOUS TIME SYSTEMS; DISTURBANCE REJECTION; GAME THEORY; NONLINEAR CONTROL SYSTEMS; OPTIMAL CONTROL SYSTEMS; ROBUSTNESS (CONTROL SYSTEMS); STOCHASTIC CONTROL SYSTEMS;

DUALITY PROPERTIES; MINIMAX GAMES; PAY-OFF; RELATIVE ENTROPY; WIDE-SENSE CONTROL LAWS;

UNCERTAIN SYSTEMS;

EID: 34247200371     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2007.894517     Document Type: Article

References (33)

1. G. Zames, "Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses," IEEE Trans. Autom. Control, vol. AC-26, no. 2, pp. 301-320, Apr. 1981.
2. J. Willems, "Dissipative dynamical systems part I: General theory," Arch. Rational Mech. Anal., vol. 45, pp. 321-351, 1972.
3. ∞ control," IEEE Trans. Autom. Control, vol. 37, no. 6, pp. 770-784, Jun. 1992.
4. ∞ - Control via measurement feedback in nonlinear systems," IEEE Trans. Autom. Control, vol. 37, no. 9, pp. 1283-1293, Sep. 1992.
5. D. Jacobson, "Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential games," IEEE Trans. Autom. Control, vol. AC-18, no. 2, pp. 124-131, Apr. 1973.
6. J. Speyer, "An adaptive terminal guidance scheme based on an exponential cost criterion with applications to homing missile guidance," IEEE Trans. Autom. Control, vol. AC-21, no. 3, pp. 371-375, Jun. 1976.
7. P. Whittle, "Risk-sensitive linear/quadratic/Gaussian control," Adv. Appl. Probab., vol. 13, pp. 764-777, 1981.
8. P. Kumar and J. van Schuppen, "On the optimal control of stochastic systems with an exponential-of-integral performance index," J. Math. Anal. Appl., vol. 80, pp. 312-332, 1981.
9. A. Bensoussan and J. H. van Schuppen, "Optimal control of partially observable stochastic systems with an exponential-of-integral performance index," SIAM J. Control Optim., vol. 23, no. 4, pp. 599-613, 1985.
10. ∞-norm bound and relations to risk-sensitivity," Syst. Control Lett., vol. 11, pp. 167-172, 1988.
11. P. Whittle, "A risk-sensitive maximum principle," Syst. Control Lett., vol. 15, pp. 183-192, 1990.
12. P. Whittle, "A risk-sensitive maximum principle: The case of imperfect state observations," IEEE Trans. Autom. Control, vol. 36, no. 7, pp. 793-801, Jul. 1991.
13. W. H. Fleming and W. M. McEneaney, "Risk-sensitive control and differential games," in Stochastic Theory and Adaptive Control, T. E. Duncan and B. Pasik-Duncan, Eds. New York: Springer-Verlag, 1992, pp. 185-197.
14. A. Lim and X. Y. Zhou, "Risk-sensitive control with HARA utility," IEEE Trans. Autom. Control, vol. 46, no. 4, pp. 563-578, Apr. 2001.
15. M. James, J. Baras, and R. Elliott, "Risk-sensitive control and dynamic games for partially observed discrete-time nonlinear systems," IEEE Trans. Autom. Control, vol. 39, no. 4, pp. 780-792, Apr. 1994.
16. C. Charalambous and J. Hibey, "Minimum principle for partially observable nonlinear risk-sensitive control problems using measure-valued decompositions," Stoch. Stoch. Rep., vol. 57, 1996.
17. C. Charalambous, "The role of informations state and adjoint in relating nonlinear output feedback risk-sensitive control and dynamic games," IEEE Trans. Autom. Control, vol. 42, no. 8, pp. 1163-1170, Aug. 1997.
18. P. D. Pra, L. Meneghini, and W. Runggaldier, "Some connections between stochastic control and dynamic games," Math. Control, Signals, Syst., vol. 9, pp. 303-326, 1996.
19. R. Elliott, L. Aggoun, and J. Moore, Hidden Markov Models Estimation and Control. New York: Springer-Verlag, 1995.
20. S. Dey and J. B. Moore, "Risk-sensitive filtering and smoothing via reference probability methods," IEEE Trans. Autom. Control, vol. 42, no. 11, pp. 1587-1591, Nov. 1997.
21. R. E. Mortensen, "Stochastic optimal control with noisy observations," Int. J. Control, vol. 4, pp. 455-464, 1966.
22. V. E. Benes and I. Karatzas, "On the relation of Zakai's and Mortensen's equations," SIAM J. Control Optim., vol. 21, no. 3, pp. 472-489, 1983.
23. W. H. Fleming and E. Pardoux, "Optimal control of partially observed diffusions," SIAM J. Control Optim., vol. 20, no. 2, pp. 261-285, 1982.
24. P. Dupuis and R. S. Ellis, A Weak Convergence Approach to the Theory of Large Deviations. New York: Wiley, 1997.
25. D. G. Luenberger, Optimization by Vector Space Methods. New York: Springer-Verlag, 1995.
26. V. A. Ugrinovskii and I. R. Petersen, "Finite horizon minimax optimal control of stochastic partially observed time varying systems," Math. Control, Signals, Syst., vol. 12, pp. 1-23, 1999.
27. I. R. Petersen, M. R. James, and P. Dupuis, "Minimax optimal control of stochastic uncertain systems with relative constraints," IEEE Trans. Autom. Control, vol. 45, no. 3, pp. 398-412, Mar. 2000.
28. P. Billingsley, Convergence of Probability Measures. New York: John Wiley, 1968.
29. W. W. Stroock and S. R. S. Varadhan, Multidimensional Diffusion Processes. New York: Springer-Verlag, 1979.
30. F. Rezaei and C. D. Charalambous, "Robust coding for uncertain sources: A minimax approach," in Proc. IEEE Int. Symp. Information Theory, Adelaide, Australia, Sep. 4-9, 2005, pp. 1539-1543.
31. C. D. Charalambous, R. Elliott, and V. Krishnamurthy, "Conditional moment generating functions for integrals and stochastic integrals," SIAM J. Control Optim., vol. 2, no. 5, pp. 1578-1603, 2004.
32. C. D. Charalambous, F. Rezaei, and A. Kyprianou, "Relations between information theory, robustness and statistical mechanics of stochastic uncertain systems via large deviations theory," in Model Reduction and Coarse-Scaling Approaches for Multiscale Phenomena, A. N. Gorban, N. Kazantzis, Y. G. Kevrekidis, H. C. Ottinger, and C. Theodoropoulos, Eds. New York: Springer-Verlag, 2006.
33. C. D. Charalambous, D. Stojan, and C. Constantinou, "Information capacity for MIMO channels with relative entropy constraint," in Proc. IEEE Int. Symp. Information Theory, Seattle, WA, Jul. 9-14, 2006, pp. 876-880.