Information geometry for control of some stochastic processes

Dodson, CTJ Information geometry for control of some stochastic processes. J. Math. Sciences. (In Press)

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Abstract

A basic requirement in control systems is a metric that measures discrepancies between actual and desired states. For statistically influenced systems information geometric methods provide natural Riemannian metrics on smooth spaces of states; such manifolds arise in minimum-phase linear systems and multi-input systems with known stochastic noise. Commonly recurring practical situations are `nearly' Poisson or `nearly' Uniform with a complementarity in the geometry of these two; another involves multivariate Gaussians and their mixtures. Similarly we encounter `nearly' independent Poisson, and `nearly' independent Gaussian processes. For such cases we have information geometric results and examples. Some of these methods are applicable to control systems for statistically influenced processes, such as monitoring essential features in continuous production of threads, films, foils and fibre networks, and batch processing of stochastic textures.

Item Type:	Article
Additional Information:	Translated from Itogi Nauki i Tekhnik, Seriya Sovremennaya Matematika i Ee Prizozheniya. Mathematical Physics, 137, 157-167 2017.
Uncontrolled Keywords:	information metric, statistical state space, geometry of near-random, near-uniform, multivariate Gaussians, mixture distributions
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User:	Prof CTJ Dodson
Date Deposited:	12 Feb 2022 19:33
Last Modified:	12 Feb 2022 19:33
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2847

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