论文标题
秘密控制线性系统
Covertly Controlling a Linear System
论文作者
论文摘要
考虑秘密控制线性系统的问题。在这个问题中，爱丽丝希望控制（稳定或更改）线性系统的参数，同时保持观察者威利（Willie），无法决定该系统是否确实受到控制。 我们正式定义了问题，在两个不同的模型下：（i）当威利只能观察系统的输出（ii）时，威利才能直接观察控制信号。专注于AR（1）系统，我们表明当Willie通过干净的通道观察系统的输出时，就无法稳定固有的不稳定线性系统。但是，从秘密地改变其参数的意义上，可以秘密地控制固有的稳定线性系统。此外，我们给出了两个重要控制器的直接和相反的结果：一个最小信息控制器，在该控制器中，爱丽丝只能在每个样本中只使用$ 1 $位，以及最大信息控制器，在该控制器中，允许爱丽丝查看现实价值的输出。与秘密交流（在费率和秘密之间取舍的情况下，结果都显示出有趣的\ emph {三折}交易 - 掩盖控制中的交易：控制器使用的信息量，控制性能和秘密性。据我们所知，这是第一个正式定义秘密控制的研究。
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.
