网络化线性系统中的状态保密码
State-Secrecy Codes for Networked Linear Systems
AI总结：
本文研究了在存在被动窃听者的情况下远程状态估计问题，提出了一种新型的状态保密码，通过用户确认信号和线性时变变换提升系统安全性与效率。
摘要：
本文研究了在存在被动窃听者的情况下远程状态估计问题。授权用户基于传感器接收到的数据估计不稳定线性系统的状态，同时数据可能被窃听者截获。本文旨在设计一种在传感器处的编码方案，以干扰窃听者的估计性能，同时使用户能够成功解码发送的消息。我们引入了一种新型的码类，称为状态保密码，利用用户确认信号并应用线性时变变换到当前和之前接收到的状态。通过利用系统过程噪声、信道物理模型和动态特性，这些码能够快速、高效，从而适用于实时动态系统。我们证明，在最简条件下，状态保密码实现完美保密，即窃听者的估计误差几乎必然无界增长，而用户的估计性能是最佳的。这些条件仅要求至少一次用户接收到对应的包而窃听者未能截获。即使一次发生此事件，窃听者的误差也会无界增长，以渐近最优的速率增加。状态保密码针对两种情况提供并研究：i) 当可以直接获得状态测量时，以及 ii) 只有输出测量可用时。理论结果通过模拟进行说明。
英文摘要：
In this paper, we study the problem of remote state estimation, in the presence of a passive eavesdropper. An authorized user estimates the state of an unstable linear plant, based on the packets received from a sensor, while the packets may also be intercepted by the eavesdropper. Our goal is to design a coding scheme at the sensor, which encodes the state information, in order to impair the eavesdropper's estimation performance, while enabling the user to successfully decode the sent messages. We introduce a novel class of codes, termed State-Secrecy Codes, which use acknowledgment signals from the user and apply linear time-varying transformations to the current and previously received states. By exploiting the properties of the system's process noise, the channel physical model and the dynamics, these codes manage to be fast, efficient and, thus, suitable for real-time dynamical systems. We prove that under minimal conditions, State-Secrecy Codes achieve perfect secrecy, namely the eavesdropper's estimation error grows unbounded almost surely, while the user's estimation performance is optimal. These conditions only require that at least once, the user receives the corresponding packet while the eavesdropper fails to intercept it. Even one occurrence of this event renders the eavesdropper's error unbounded with asymptotically optimal rate of increase. State-Secrecy Codes are provided and studied for two cases, i) when direct state measurements are available, and ii) when we only have output measurements. The theoretical results are illustrated in simulations.
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