This paper is motivated by the increasing security concerns of cyber-physical systems. Here, we develop a discretization-free verification scheme targeting an information-flow security property, called approximate initial-state opacity, for the class of discrete-time control systems. We propose notions of so-called augmented control barrier certificates in conjunction with specified regions of interest capturing the initial and secret sets of the system. Sufficient conditions for (the lack of) approximate initial-state opacity of discrete-time control systems are proposed based on the existence of the proposed barrier certificates. We further present an efficient computation method by casting the conditions for barrier certificates as sum-of-squares programming problems. The effectiveness of the proposed results is illustrated through two numerical examples.

中文翻译：

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通过屏障证书验证近似不透明度

这篇论文的动机是对网络物理系统的安全问题日益关注。在这里，我们针对离散时间控制系统类的信息流安全属性（称为近似初始状态不透明度）开发了一种无离散化验证方案。我们提出了所谓的增强控制屏障证书的概念，结合特定的兴趣区域捕获系统的初始和秘密集。基于所提出的屏障证书的存在，提出了离散时间控制系统的（缺乏）近似初始状态不透明度的充分条件。我们通过将障碍证书的条件转换为平方和规划问题，进一步提出了一种有效的计算方法。