Minimizing Control Attention:The Linear Gauss-Markov paradigm
Abstract
We revisit the concept of `attention' as a technical term to quantify the effort in calibrating control action based on available data. While Wiener, in his work on Cybernetics, anticipated key principles on prioritizing task-relevant signals, it was not until the late 1990's when Brockett first formulated pertinent optimization problems that have inspired subsequent as well as the present work. `Attention,' as a technical term, is defined so as to quantify the dependence of the control law on the time and space/state coordinate; a control law that is independent of time and space, assuming it meets specifications, requires vanishing attention. In the present work we focus on Linear-Markovian dynamics with Gaussian state uncertainty so as to analyze the structure of minimal-attention control schemes that steer the dynamics between terminal states with Gaussian uncertainty profile.
Keywords
Cite
@article{arxiv.2512.07046,
title = {Minimizing Control Attention:The Linear Gauss-Markov paradigm},
author = {Ralph Sabbagh and Asmaa Eldesoukey and Mahmoud Abdelgalil and Tryphon T. Georgiou},
journal= {arXiv preprint arXiv:2512.07046},
year = {2025}
}