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An information geometry algorithm for distribution control

An information geometry algorithm for distribution control In this paper, we consider the problem of distribution control from the viewpoint of information geometry. Different from most existing models used in stochastic control, it is assumed that the control input directly affects the distribution of the system output in probability sense. Here, we set up a new manifold (S), meanwhile the B-spline manifold (B) and the system output manifold (M) can be referred to as its submanifolds. We give an information geometrical algorithm which can be called as geodesic-projection algorithm using the properties of manifold. In the geodesic step, we can obtain the geodesic equation from the initial point V 0 = (ω 10, ω 20, ··· , ω (n−1)0) to the specified point V g = (ω 1g , ω 2g , ··· , ω (n−1)g ) in B. This gives us an optimal trajectory for the points changing along in B. In the projection step, we project the sample points selected from the geodesic onto M. The coordinates of the projections in M give the trajectory of the control input u. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

An information geometry algorithm for distribution control

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References (9)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-008-0068-3
Publisher site
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Abstract

In this paper, we consider the problem of distribution control from the viewpoint of information geometry. Different from most existing models used in stochastic control, it is assumed that the control input directly affects the distribution of the system output in probability sense. Here, we set up a new manifold (S), meanwhile the B-spline manifold (B) and the system output manifold (M) can be referred to as its submanifolds. We give an information geometrical algorithm which can be called as geodesic-projection algorithm using the properties of manifold. In the geodesic step, we can obtain the geodesic equation from the initial point V 0 = (ω 10, ω 20, ··· , ω (n−1)0) to the specified point V g = (ω 1g , ω 2g , ··· , ω (n−1)g ) in B. This gives us an optimal trajectory for the points changing along in B. In the projection step, we project the sample points selected from the geodesic onto M. The coordinates of the projections in M give the trajectory of the control input u.

Journal

Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals

Published: Mar 4, 2016

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