Information Geometry Control under the Laplace Assumption

By combining information science and differential geometry, information geometry provides a geometric method to measure the differences in the time evolution of the statistical states in a stochastic process. Specifically, the so-called information length (the time integral of the information rate) describes the total amount of statistical changes that a time-varying probability distribution takes through time. In this work, we outline how the application of information geometry may permit us to create energetically efficient and organised behaviour artificially. Specifically, we demonstrate how nonlinear stochastic systems can be analysed by utilising the Laplace assumption to speed up the numerical computation of the information rate of stochastic dynamics. Then, we explore a modern control engineering protocol to obtain the minimum statistical variability while analysing its effects on the closed-loop system’s stochastic thermodynamics.