Information Transfer in Dynamical Systems and Optimal Placement of Actuators and Sensors for Control of Non-equilibrium Dynamics

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2019-09-29
Authors
Vaidya, Umesh
Sinha, Subhrajit
Vaidya, Umesh
Yeung, Enoch
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Electrical and Computer Engineering
Abstract

In this paper we develop the concept of information transfer between the Borel-measurable sets for a dynamical system described by a measurable space and a non-singular transformation. The concept is based on how Shannon entropy is transferred between the measurable sets, as the dynamical system evolves. We show that the proposed definition of information transfer satisfies the usual notions of information transfer and causality, namely, zero transfer and transfer asymmetry. Furthermore, we show how the information transfer measure can be used to classify ergodicity and mixing. We also develop the computational methods for information transfer computation and apply the framework for optimal placements of actuators and sensors for control of non-equilibrium dynamics.

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This is a pre-print of the article Sinha, Subhrajit, Umesh Vaidya, and Enoch Yeung. "Information Transfer in Dynamical Systems and Optimal Placement of Actuators and Sensors for Control of Non-equilibrium Dynamics." arXiv preprint arXiv:1909.13369 (2019). Posted with permission.

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