### Abstract

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 [1] and [2] between risk-sensitive and H_{∞}-robust control from finite to infinite dimensional spaces.

Original language | English (US) |
---|---|

Pages (from-to) | 2184-2186 |

Number of pages | 3 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 3 |

State | Published - 1994 |

Externally published | Yes |

Event | Proceedings of the 2nd IEEE International Symposium on Requirements Engineering - York, Engl Duration: Mar 27 1995 → Mar 29 1995 |

## Fingerprint Dive into the research topics of 'Risk-sensitive control, differential games, and limiting problems in infinite dimensions'. Together they form a unique fingerprint.

## Cite this

*Proceedings of the IEEE Conference on Decision and Control*,

*3*, 2184-2186.