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

TL;DR

This paper introduces a novel information transfer measure for dynamical systems based on Shannon entropy, enabling classification of ergodicity and mixing, and optimizing actuator and sensor placement for controlling non-equilibrium dynamics.

Contribution

It develops a new measure of information transfer for dynamical systems and applies it to optimal sensor and actuator placement for controlling non-equilibrium dynamics.

Findings

The measure satisfies causality and transfer asymmetry.

It can classify ergodicity and mixing.

Applied to optimize actuator and sensor placement.

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.