## Abstract

The standard definition of the stochastic risk-sensitive linear-quadratic (RS-LQ) control depends on the risk parameter, which is normally left to be set exogenously. We reconsider the classical approach and suggest two alternatives, resolving the spurious freedom naturally. One approach consists in seeking for the minimum of the tail of the probability distribution function (PDF) of the cost functional at some large fixed value. Another option suggests minimizing the expectation value of the cost functional under a constraint on the value of the PDF tail. Under the assumption of resulting control stability, both problems are reduced to static optimizations over a stationary control matrix. The solutions are illustrated using the examples of scalar and 1D chain (string) systems. The large deviation self-similar asymptotic of the cost functional PDF is analyzed.

Original language | English (US) |
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Article number | P08007 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2012 |

Issue number | 8 |

DOIs | |

State | Published - Aug 2012 |

Externally published | Yes |

## Keywords

- large deviations in non-equilibrium systems
- robust and stochastic optimization

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty