Bellman Equations of Risk-Sensitive Control
- 1 January 1996
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control and Optimization
- Vol. 34 (1) , 74-101
- https://doi.org/10.1137/s0363012993255302
Abstract
Risk-sensitive control problems are considered. Existence of a nonnegative solution to the Bellman equation of risk-sensitive control is shown. The result is applied to prove that no breaking down occurs. Asymptotic behaviour of the nonnegative solution is studied in relation to ergodic control problems and the relationship between the asymptotics and the large deviation principle is noted.Keywords
This publication has 16 references indexed in Scilit:
- An ergodic control problem arising from the principal eigenfunction of an elliptic operatorJournal of the Mathematical Society of Japan, 1991
- Heat Kernels and Spectral TheoryPublished by Cambridge University Press (CUP) ,1989
- State-space formulae for all stabilizing controllers that satisfy an H∞-norm bound and relations to relations to risk sensitivitySystems & Control Letters, 1988
- Optimal Control of Partially Observable Stochastic Systems with an Exponential-of-Integral Performance IndexSIAM Journal on Control and Optimization, 1985
- Problèmes de Neumann quasilinéairesJournal of Functional Analysis, 1985
- Stochastic stability of differential equationsPublished by Springer Nature ,1980
- Controlled Diffusion ProcessesPublished by Springer Nature ,1980
- On the principal eigenvalue of second‐order elliptic differential operatorsCommunications on Pure and Applied Mathematics, 1976
- Asymptotic evaluation of certain Markov process expectations for large time—IIICommunications on Pure and Applied Mathematics, 1976
- Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential gamesIEEE Transactions on Automatic Control, 1973