In this paper we present the solutions of the stochastic finite and infinite horizon risk-sensitive control problems in infinite dimensions, with μ, ε > 0, respectively, representing the risk-sensitivity and small noise parameters. Invoking a logarithmic transformation, a stochastic differential game equivalent to the risk-sensitive problem is obtained. In the limit as ε ↓ 0, the deterministic differential game associated with the H∞-disturbance attenuation control problem of distributed parameter systems is recovered. In the limit as μ ↓ 0 (resp. μ ↓ 0, ε ↓ 0) the usual stochastic (resp. deterministic) control problem with integral cost is recovered. Both finite and infinite horizon cases are treated. This article extends the recent relations  and  between risk-sensitive and H∞-robust control from finite to infinite dimensional spaces.
|Original language||English (US)|
|Number of pages||3|
|Journal||Proceedings of the IEEE Conference on Decision and Control|
|State||Published - 1994|
|Event||Proceedings of the 2nd IEEE International Symposium on Requirements Engineering - York, Engl|
Duration: Mar 27 1995 → Mar 29 1995