Title: Covertly Controlling a Linear System Show Chinese title

Title: 隐蔽地控制一个线性系统

Abstract: 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 can not be covertly stabilized. However, 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. 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. Show Chinese abstract

Abstract: 考虑对线性系统进行隐蔽控制的问题。 在这个问题中，Alice希望控制（稳定或改变行为）一个线性系统，同时让观察者Willie无法判断系统是否真的被控制。 我们在一个模型下正式定义了这个问题，其中Willie只能观察系统的输出。 聚焦于AR(1)系统，我们证明了当Willie通过干净信道观察系统输出时，固有不稳定的线性系统无法被隐蔽地稳定。 然而，固有稳定的线性系统可以被隐蔽地控制，在隐蔽地改变其参数或重置其记忆的意义上。 此外，我们给出了两个重要控制器的正负结果：一个最小信息控制器，其中Alice每样本只能使用$1$位，以及一个最大信息控制器，其中Alice可以查看实数值输出。 与隐蔽通信不同，隐蔽通信中的权衡是速率和隐蔽性之间的权衡，而结果揭示了隐蔽控制中一个有趣的\emph{三重的}权衡：控制器使用的的信息量、控制性能和隐蔽性。