Covertly Controlling a Linear System

TL;DR

This paper introduces the concept of covert control of linear systems, analyzing how to manipulate system parameters without detection, revealing fundamental limits and trade-offs in covert stabilization and control.

Contribution

It formally defines the problem of covert control, analyzes its fundamental limits for AR(1) systems, and explores the trade-offs between information, control performance, and covertness.

Findings

Unstable systems cannot be covertly stabilized when observed through a clean channel.

Stable systems can be covertly controlled to change parameters.

There is a three-fold trade-off among information used, control performance, and covertness.

Abstract

Consider the problem of covertly controlling a linear system. In this problem, Alice desires to control (stabilize or change the parameters of) a linear system, while keeping an observer, Willie, unable to decide if the system is indeed being controlled or not. We formally define the problem, under two different models: (i) When Willie can only observe the system's output (ii) When Willie can directly observe the control signal. Focusing on AR(1) systems, we show that when Willie observes the system's output through a clean channel, an inherently unstable linear system can not be covertly stabilized. However, an inherently stable linear system can be covertly controlled, in the sense of covertly changing its parameter. Moreover, we give direct and converse results for two important controllers: a minimal-information controller, where Alice is allowed to used only $1$ bit per sample, and a maximal-information controller, where Alice is allowed to view the real-valued output. Unlike covert communication, where the trade-off is between rate and covertness, the results reveal an interesting \emph{three--fold} trade--off in covert control: the amount of information used by the controller, control performance and covertness. To the best of our knowledge, this is the first study formally defining covert control.