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.
翻译:考虑隐蔽控制线性系统的问题。 在这个问题中,爱丽丝希望控制(稳定或改变)线性系统(稳定或改变)线性系统的参数,同时保持观察者威利无法决定系统是否受到控制。我们正式根据两种不同模式来定义问题:(一) 当威利只能观察系统输出时;(二) 当威利能够直接观察控制信号时;(二) 当威利能够直接观察AR(1)系统时,我们显示,当威利通过清洁通道观察系统输出时,一个内在不稳定的线性系统不能被秘密稳定。然而,一个内在稳定的线性系统可以被秘密控制,从隐蔽改变其参数的意义上说。此外,我们给两个重要控制者提供了直接和反向的结果:一个最小的信息控制者,允许爱丽丝只使用每样只1美元,一个最大信息控制器,允许爱丽丝查看真实价值产出。与隐蔽通信不同,在率和隐蔽之间,结果显示一个有趣的\emph{3x) 。结果显示一个内在稳定的线性系统可以秘密控制。此外,我们最隐蔽的控制者将确定我们所使用的控制。