### Abstract

In this paper, we propose a steepest descent algorithm based on the natural gradient to design the controller of an open-loop stochastic distribution control system (SDCS) of multi-input and single output with a stochastic noise. Since the control input vector decides the shape of the output probability density function (PDF), the purpose of the controller design is to select a proper control input vector, so that the output PDF of the SDCS can be as close as possible to the target PDF. In virtue of the statistical characterizations of the SDCS, a new framework based on a statistical manifold is proposed to formulate the control design of the input and output SDCSs. Here, the Kullback-Leibler divergence is presented as a cost function to measure the distance between the output PDF and the target PDF. Therefore, an iterative descent algorithm is provided, and the convergence of the algorithm is discussed, followed by an illustrative example of the effectiveness.

Original language | English |
---|---|

Pages (from-to) | 4338-4352 |

Number of pages | 15 |

Journal | Entropy |

Volume | 16 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- Kullback-Leibler divergence
- Natural gradient algorithm
- Stochastic distribution control system

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Entropy*,

*16*(8), 4338-4352. https://doi.org/10.3390/e16084338

**A natural gradient algorithm for stochastic distribution systems.** / Zhang, Zhenning; Sun, Huafei; Peng, Linyu; Jiu, Lin.

Research output: Contribution to journal › Article

*Entropy*, vol. 16, no. 8, pp. 4338-4352. https://doi.org/10.3390/e16084338

}

TY - JOUR

T1 - A natural gradient algorithm for stochastic distribution systems

AU - Zhang, Zhenning

AU - Sun, Huafei

AU - Peng, Linyu

AU - Jiu, Lin

PY - 2014

Y1 - 2014

N2 - In this paper, we propose a steepest descent algorithm based on the natural gradient to design the controller of an open-loop stochastic distribution control system (SDCS) of multi-input and single output with a stochastic noise. Since the control input vector decides the shape of the output probability density function (PDF), the purpose of the controller design is to select a proper control input vector, so that the output PDF of the SDCS can be as close as possible to the target PDF. In virtue of the statistical characterizations of the SDCS, a new framework based on a statistical manifold is proposed to formulate the control design of the input and output SDCSs. Here, the Kullback-Leibler divergence is presented as a cost function to measure the distance between the output PDF and the target PDF. Therefore, an iterative descent algorithm is provided, and the convergence of the algorithm is discussed, followed by an illustrative example of the effectiveness.

AB - In this paper, we propose a steepest descent algorithm based on the natural gradient to design the controller of an open-loop stochastic distribution control system (SDCS) of multi-input and single output with a stochastic noise. Since the control input vector decides the shape of the output probability density function (PDF), the purpose of the controller design is to select a proper control input vector, so that the output PDF of the SDCS can be as close as possible to the target PDF. In virtue of the statistical characterizations of the SDCS, a new framework based on a statistical manifold is proposed to formulate the control design of the input and output SDCSs. Here, the Kullback-Leibler divergence is presented as a cost function to measure the distance between the output PDF and the target PDF. Therefore, an iterative descent algorithm is provided, and the convergence of the algorithm is discussed, followed by an illustrative example of the effectiveness.

KW - Kullback-Leibler divergence

KW - Natural gradient algorithm

KW - Stochastic distribution control system

UR - http://www.scopus.com/inward/record.url?scp=84905716067&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84905716067&partnerID=8YFLogxK

U2 - 10.3390/e16084338

DO - 10.3390/e16084338

M3 - Article

AN - SCOPUS:84905716067

VL - 16

SP - 4338

EP - 4352

JO - Entropy

JF - Entropy

SN - 1099-4300

IS - 8

ER -