Information Geometry Control under the Laplace Assumption

Guel-Cortez, Adrián-Josué; Kim, Eun Jin

doi:10.3390/psf2022005025

Cited by 2 publications

(1 citation statement)

References 23 publications

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“…In the future, we plan to explore further connections with the area of control theory for applications in more complex scenarios. For instance, we can extend our results to non-linear systems by employing approximation methods such as the Laplacian assumption [48][49][50]. Then, we can utilise modern control techniques such as the model-predictive-control [51,52] to find the solution to the proposed optimisation problems J 1 and J 2 .…”

Section: Discussionmentioning

confidence: 98%

Relations between entropy rate, entropy production and information geometry in linear stochastic systems

Guel-Cortez¹,

Kim²

2023

J. Stat. Mech.

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In this work, we investigate the relation between the concept of ‘information rate’, an information geometric method for measuring the speed of the time evolution of the statistical states of a stochastic process, and stochastic thermodynamics quantities like entropy rate and entropy production. Then, we propose the application of entropy rate and entropy production to different practical applications such as abrupt event detection, correlation analysis, and control engineering. Specifically, by utilising the Fokker–Planck equation of multi-variable linear stochastic processes described by Langevin equations, we calculate the exact value for information rate, entropy rate, and entropy production and derive various inequalities among them. Inspired by classical correlation coefficients and control techniques, we create entropic-informed correlation coefficients as abrupt event detection methods and information geometric cost functions as optimal thermodynamic control policies, respectively. The methods are analysed via the numerical simulations of common prototypical systems.

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Section: Discussionmentioning

confidence: 98%

Relations between entropy rate, entropy production and information geometry in linear stochastic systems

Guel-Cortez¹,

Kim²

2023

J. Stat. Mech.

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Minimum Information Variability in Linear Langevin Systems via Model Predictive Control

Guel-Cortez,

Kim,

Mehrez

2024

Entropy

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Controlling the time evolution of a probability distribution that describes the dynamics of a given complex system is a challenging problem. Achieving success in this endeavour will benefit multiple practical scenarios, e.g., controlling mesoscopic systems. Here, we propose a control approach blending the model predictive control technique with insights from information geometry theory. Focusing on linear Langevin systems, we use model predictive control online optimisation capabilities to determine the system inputs that minimise deviations from the geodesic of the information length over time, ensuring dynamics with minimum “geometric information variability”. We validate our methodology through numerical experimentation on the Ornstein–Uhlenbeck process and Kramers equation, demonstrating its feasibility. Furthermore, in the context of the Ornstein–Uhlenbeck process, we analyse the impact on the entropy production and entropy rate, providing a physical understanding of the effects of minimum information variability control.

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Information Geometry Control under the Laplace Assumption

Cited by 2 publications

References 23 publications

Relations between entropy rate, entropy production and information geometry in linear stochastic systems

Relations between entropy rate, entropy production and information geometry in linear stochastic systems

Minimum Information Variability in Linear Langevin Systems via Model Predictive Control

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