Minimizing Control Attention:The Linear Gauss-Markov paradigm

TL;DR

This paper explores the concept of attention in control systems, focusing on linear-Markovian dynamics with Gaussian noise, to identify minimal-attention control strategies that efficiently steer states between targets.

Contribution

It introduces a formal definition of attention in control laws and analyzes minimal-attention schemes within linear-Gaussian frameworks, building on foundational optimization principles.

Findings

Characterization of minimal-attention control laws

Analysis of control effort versus attention dependence

Framework for designing attention-efficient control strategies

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.