Covertly Controlling a Linear System

Consider the problem of covertly controlling a linear system. In this problem, Alice desires to control (stabilize or change the behavior 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 a model where Willie can only observe the system's output. Focusing on AR(1) systems, we show that when Willie observes the system's output through a clean channel, an inherently unstable linear system cannot be covertly stabilized. However, under some conditions on the parameters and observation time, an inherently stable linear system can be covertly controlled, in the sense of covertly changing its parameter or resetting its memory. Moreover, we give positive and negative results for two important controllers: a minimal-information controller, where Alice is allowed to use only 1 bit per sample, and a maximal-information controller, where Alice is allowed to view the real-valued output. The results reveal an interesting interplay in covert control, between the amount of information used by the c ontroller, control performance and covertness.