Risk-sensitive control, differential games, and limiting problems in infinite dimensions
AuthorCharalambous, Charalambos D.
Moore, Kevin L.
SourceProceedings of the IEEE Conference on Decision and Control
Proceedings of the IEEE Conference on Decision and Control
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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.
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