A natural gradient algorithm for stochastic distribution systems

Zhenning Zhang, Huafei Sun*, Linyu Peng, Lin Jiu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 languageEnglish
Pages (from-to)4338-4352
Number of pages15
Issue number8
Publication statusPublished - 2014


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

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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