Bellman equations of risk-sensitive control

SIAM Journal on Control and Optimization

Volumn 34, Issue 1, 1996, Pages 74-101

  Nagai, H ^a  

^a OSAKA UNIVERSITY   (Japan)

Author keywords

Asymptotic behaviour; Bellman equation; Breaking down; Ergodic control; Large deviation; Risk sensitive control

Indexed keywords

ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; FUNCTIONS; PARAMETER ESTIMATION; PROBABILITY; STOCHASTIC CONTROL SYSTEMS;

ASYMPTOTICS; BELLMAN EQUATIONS; BREAKING DOWN; ERGODIC CONTROL; LARGE DEVIATION PRINCIPLE; NONNEGATIVE SOLUTION; RISK SENSITIVE CONTROL;

CONTROL THEORY;

EID: 0029778591     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012993255302     Document Type: Article

References (25)

1. A. BENSOUSSAN AND J. FREHSE, On Bellman equations of ergodic type with quadratic growth Hamiltonian, Pitman Res. Notes Math. Ser., 148 (1987), pp. 13-26.
2. N, J. Reine Angew. Math., 429 (1992), pp. 125-160.
3. 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., 23 (1985), pp. 599-613.
4. A. BENSOUSSAN AND H. NAGAI, An ergodic control problem arising from the principal eigenfunction of an elliptic operator, J. Math. Soc. Japan, 43 (1991), pp. 49-65.
5. E. B. DAVIES, Heat Kernels and Spectral Theory, Cambridge University Press, London, 1989.
6. J. M. DEUSCHEL AND D. W. STROOCK, Large Deviations, Academic Press, New York, 1989.
7. M. D. DONSKER AND S. R. S. VARADHAN, Asymptotic evaluation of certain Markov process expectation for large time, III, Comm. Pure Appl. Math., 29 (1976), pp. 389-461.
8. _, On the principal eigenvalue of second-order elliptic differential operators, Comm. Pure Appl. Math., 29 (1976), pp. 595-621.
9. W. H. FLEMING AND W. M. MCENEANEY, Risk sensitive control with ergodic cost criteria, Proc. 31th CDC Conference, Tucson, AZ, 1992, pp. 2048-2052.
10. M. FUKUSHIMA, Dirichlet Forms and Markov Processes, North Holland-Kodansha, Amsterdam, 1980.
11. F. GIMBERT, Problemes de Neumann quasilineaires, J. Funct. Anal., 68 (1985), pp. 65-72.
12. ∞-norm bound and relation to risk sensitivity, Systems Control Lett., 11 (1986), pp. 167-172.
13. R. Z. HAS'MINSKII, Stochastic Stability of Differential Equations, Sijthoff Noordhoff, Alphen aan den Rijn, 1980.
14. N. IKEDA AND S. WATANABE, Stochastic Differential Equations and Diffusion Processes, North Holland-Kodansha, Amsterdam, 1989.
15. D. H. JACOBSON, Optimal stochastic linear systems with exponential performance criteria and relation to deterministic differential games, IEEE Trans. Automat. Control, AC-18 (1973), pp. 124-131.
16. N. V. KRYLOV, Controlled diffusion processes, Springer-Verlag, New York, Heidelberg, Berlin, 1980.
17. O. A. LADYZENSKAYA, V. A. SOLONIKOV, AND N. N. URAL'CEVA, Linear and Quasilinear Equations of Parabolic Type, AMS Transl. of Math. Monographs, Providence, RI, 1968.
18. P. LI AND S. T. YAU, On the parabolic kernel of the Schrödinger operator, Acta Math., 156 (1986), pp. 153-201.
19. P. L. LIONS, Quelques remarques sur les problemes elliptiques quasi lineaires du second ordre, J. d'Analyse Math., 45 (1985), pp. 234-254.
20. R. S. LIPTSER AND A. N. SHIRYAEV, Statistics of Random Processes I, Springer-Verlag, New York, 1977.
21. H. NAGAI, Ergodic control problems on the whole Euclidean space and convergence of symmetric diffusions, Forum Math., 4 (1992), pp. 159-173.
22. _, A remark on parabolic Harnack inequalities, Bull. London Math. Soc., 24 (1992), pp. 469-474.
23. T. RUNOLFSSON, Stationary risk-sensitive LQG control and its relation to LQG and H-infinity control, Proc. 29th CDC Conference, Honolulu, HI, 1990, pp. 1018-1023.
24. D. W. STROOCK AND S. R. S. VARADHAN, Multidimensional Diffusion Processes, Springer-Verlag, New York, 1979.
25. P. WHITTLE, Risk-sensitive linear/quadratic/Gaussian control, Adv. Appl. Prob., 13 (1981), pp. 764-777.