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.
Highlights
Information geometry [1,2,3,4,5,6] proposed by some scholars has been widely applied to various fields, such as neural network [7,8], control systems [9,10,11,12], dynamical system [13,14] and information science [15,16]
In [22], the authors firstly brought the idea of information geometry to the field of stochastic distribution control system (SDCS) and presented a comparative study on the parameter estimation performance between the geodesic equation and the B-spline function approximations, when the system output distributions are Gamma family distributions
We investigate more complicated SDCSs of multi-input, single output with a stochastic noise from the viewpoint of information geometry
Summary
Department of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China Department of Applied Mechanics and Aerospace Engineering & Research Institute of Nonlinear Received: 10 September 2013; in revised form: 15 July 2014 / Accepted: 28 July 2014 /
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