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Entropy 2014, 16(8), 4338-4352; doi:10.3390/e16084338

A Natural Gradient Algorithm for Stochastic Distribution Systems

1
Department of Mathematics, Beijing University of Technology, Beijing 100124, China
2
Department of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
3
Department of Applied Mechanics and Aerospace Engineering & Research Institute of Nonlinear PDEs, Waseda University, Okubo, Shinjuku, Tokyo 169-8555, Japan
4
Department of Mathematics, Tulane University, 6823 St. Charles Ave., New Orleans, LA 70118,USA
*
Author to whom correspondence should be addressed.
Received: 10 September 2013 / Revised: 15 July 2014 / Accepted: 28 July 2014 / Published: 4 August 2014
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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. View Full-Text
Keywords: stochastic distribution control system; natural gradient algorithm; Kullback–Leibler divergence stochastic distribution control system; natural gradient algorithm; Kullback–Leibler divergence
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Zhang, Z.; Sun, H.; Peng, L.; Jiu, L. A Natural Gradient Algorithm for Stochastic Distribution Systems. Entropy 2014, 16, 4338-4352.

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