# Minimum Information Variability in Linear Langevin Systems via Model Predictive Control

## TL;DR

This paper introduces a new control method for managing complex systems by minimizing changes in information over time using model predictive control and information geometry.

## Contribution

A novel control approach combining model predictive control and information geometry to minimize geometric information variability in linear Langevin systems.

## Key findings

- The method was validated on the Ornstein–Uhlenbeck process and Kramers equation, showing feasibility.
- It reduces entropy production and entropy rate in the Ornstein–Uhlenbeck process, offering physical insights.

## Abstract

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.