### Abstract

The risk-sensitive optimal stochastic control problem has an interpretation in terms of managing the value of a denumerable linear combination of the cumulants of a traditional performance index. This paper considers in detail the foundations for a full-state-feedback solution to the problem of controlling the second cumulant of a cost function, given modest constraints on the first cumulant. The formulation is carried out for a class of nonlinear stochastic differential equations, associated with an appropriate class of non-quadratic performance indices. A Hamilton-Jacobi framework is adopted, and the defining equations for solving the linear, quadratic case are determined. The method is then applied to a situation in which a building is to be protected from earthquakes.

Original language | English (US) |
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Pages (from-to) | 1036-1041 |

Number of pages | 6 |

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

Volume | 2 |

State | Published - Dec 1 1995 |

Externally published | Yes |

Event | Proceedings of the 1995 34th IEEE Conference on Decision and Control. Part 1 (of 4) - New Orleans, LA, USA Duration: Dec 13 1995 → Dec 15 1995 |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

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

*2*, 1036-1041.