A framework for opacity in linear systems
A framework for opacity in linear systems
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DOI：
10.1109/acc.2016.7526666
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发表时间：
2016-07
期刊：
影响因子：
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通讯作者：
Bhaskar Ramasubramanian;R. Cleaveland;S. Marcus
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文献类型：
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作者：
Bhaskar Ramasubramanian;R. Cleaveland;S. Marcus
提出了一种基于离散时间线性时不变系统建模的计算机物理系统不透明性框架。如果一个秘密状态的集合从时间0的这些集合开始，时间k的输出对于被动对抗性观察者是不可区分的，则关于一个非秘密状态的集合是k-ISO的。利用系统的可达集给出了k-ISO的充要条件。验证了k-ISO在并集和交集下的性质。可以看出，尽管不透明集的并集保持不透明度，但对于交叉点来说并不一定是这样。证明了在一定条件下，k-ISO等价于输出能控性。最后，在给定初始状态的候选秘密集和非秘密集的情况下，给出了一个计算k-ISO状态集的算法。
We present a framework for opacity in 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 a passive adversarial observer. Necessary and sufficient conditions for k-ISO are given in terms of reachable sets of the system. Properties of k-ISO under unions and intersections are verified. It is seen that while unions of opaque sets preserve opacity, this is not necessarily true for intersections. We show that under certain conditions, k-ISO is equivalent to output controllability. Finally, we present an algorithm to compute a k-ISO set of states, given candidate secret and nonsecret sets of initial states.