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首页> 外文期刊>IEEE Transactions on Automatic Control >Notions of Centralized and Decentralized Opacity in Linear Systems
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Notions of Centralized and Decentralized Opacity in Linear Systems

机译：线性系统中集中和分散的不透明度的概念

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We formulate notions of opacity for cyberphysical systems modeled as discrete-time linear time-invariant systems. A set of secret states is k-ISO with respect to a set of nonsecret states if, starting from these sets at time 0, the outputs at time k are indistinguishable to an adversarial observer. Necessary and sufficient conditions to ensure that a secret specification is k-ISO are established in terms of sets of reachable states. We also show how to adapt techniques for computing underapproximations and overapproximations of the set of reachable states of dynamical systems in order to soundly approximate k-ISO. Furthermore, we provide a condition for output controllability, if k-ISO holds, and show that the converse holds under an additional assumption. We extend the theory of opacity for single-adversary systems to the case of multiple adversaries and develop several notions of decentralized opacity. We study the following scenarios: first, the presence or lack of a centralized coordinator, and, second, the presence or absence of collusion among adversaries. In the case of colluding adversaries, we derive a condition for nonopacity that depends on the structure of the directed graph representing the communication between adversaries. Finally, we relax the condition that the outputs be indistinguishable and define a notion of epsilon-opacity, and also provide an extension to the case of nonlinear systems.
机译：我们制定建模为离散时间线性时不变系统cyberphysical系统透明度的概念。一组秘密状态是关于一组非本作态的k-ISO，如果从时间0开始从这些集合开始，则在时间k的输出难以区分到对手观察者。在可达状态范围内建立必要和充分的条件，以确保秘密规范是K-ISO。我们还展示了如何适应用于计算动态系统的可达状态集的低估和过度估计的技术，以便似乎近似K-ISO。此外，如果K-ISO保持，我们提供了输出可控性的条件，并显示逆转带在额外的假设下保持。我们将单对手系统的不透明度理论扩展到多个对手的情况，并制定几个分散的不透明度的概念。我们研究以下情景：首先，集中协调员的存在或缺乏，以及对手之间的存在或缺乏勾结。在勾结对手的情况下，我们得出了非易性的条件，这取决于表示对手之间的通信的定向图的结构。最后，我们放宽输出无法区分并定义epsilon - 不透明度的概念，并且还提供非线性系统情况的扩展。

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