### Abstract

We study the problem that arises in a class of stochastic processes referred to as Stochastic Hybrid Systems (SHS) when computing the moments of the states using the generator of the process and Dynkin's formula. We focus on the case when the SHS is at equilibrium or approaching equilibrium. We present a family of such processes for which infinite-dimensional linear-system analysis tools are ineffective, and discuss a few differing perspectives on how to tackle such problems by assuming that the SHS state distribution is such that its entropy is maximum. We also provide a numerical algorithm that allows us to efficiently compute maximum entropy solutions, and compare results with Monte Carlo simulations for some illustrative SHS.

Original language | English (US) |
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Article number | 7039471 |

Pages (from-to) | 747-752 |

Number of pages | 6 |

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

Volume | 2015-February |

Issue number | February |

DOIs | |

State | Published - Jan 1 2014 |

Event | 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: Dec 15 2014 → Dec 17 2014 |

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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*,

*2015-February*(February), 747-752. [7039471]. https://doi.org/10.1109/CDC.2014.7039471

**A maximum entropy approach to the moment closure problem for Stochastic Hybrid Systems at equilibrium.** / Zhang, Jiangmeng; Deville, Lee; Dhople, Sairaj; Dominguez-Garcia, Alejandro D.

Research output: Contribution to journal › Conference article

*Proceedings of the IEEE Conference on Decision and Control*, vol. 2015-February, no. February, 7039471, pp. 747-752. https://doi.org/10.1109/CDC.2014.7039471

}

TY - JOUR

T1 - A maximum entropy approach to the moment closure problem for Stochastic Hybrid Systems at equilibrium

AU - Zhang, Jiangmeng

AU - Deville, Lee

AU - Dhople, Sairaj

AU - Dominguez-Garcia, Alejandro D.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We study the problem that arises in a class of stochastic processes referred to as Stochastic Hybrid Systems (SHS) when computing the moments of the states using the generator of the process and Dynkin's formula. We focus on the case when the SHS is at equilibrium or approaching equilibrium. We present a family of such processes for which infinite-dimensional linear-system analysis tools are ineffective, and discuss a few differing perspectives on how to tackle such problems by assuming that the SHS state distribution is such that its entropy is maximum. We also provide a numerical algorithm that allows us to efficiently compute maximum entropy solutions, and compare results with Monte Carlo simulations for some illustrative SHS.

AB - We study the problem that arises in a class of stochastic processes referred to as Stochastic Hybrid Systems (SHS) when computing the moments of the states using the generator of the process and Dynkin's formula. We focus on the case when the SHS is at equilibrium or approaching equilibrium. We present a family of such processes for which infinite-dimensional linear-system analysis tools are ineffective, and discuss a few differing perspectives on how to tackle such problems by assuming that the SHS state distribution is such that its entropy is maximum. We also provide a numerical algorithm that allows us to efficiently compute maximum entropy solutions, and compare results with Monte Carlo simulations for some illustrative SHS.

UR - http://www.scopus.com/inward/record.url?scp=84988268681&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84988268681&partnerID=8YFLogxK

U2 - 10.1109/CDC.2014.7039471

DO - 10.1109/CDC.2014.7039471

M3 - Conference article

AN - SCOPUS:84988268681

VL - 2015-February

SP - 747

EP - 752

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

IS - February

M1 - 7039471

ER -