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 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 the model when 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 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 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. Unlike covert communication, where the trade-off is between rate and covertness; and in cyber-physical systems the trade-off is between control and attack detection, the results reveal an interesting 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.