发表机构
Shenyang Ligong University; Tongji University; Wayne State University（沈阳理工大学; 同济大学; 韦恩州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对网络攻击下离散事件系统，深入研究CA可观测性，提出检验算法并揭示其不封闭性，进而给出计算CA可控可观测子语言及监督器设计方法。
AI 中文摘要
在先前的一篇论文中，我们研究了网络攻击下离散事件系统的控制问题，其中提出了CA可控性和CA可观测性。我们证明，一个离散事件系统能被控制以生成规范语言K，当且仅当K是CA可控且CA可观测的。虽然CA可控性可以“转换”为（传统）可控性，但CA可观测性不能“转换”为（传统）可观测性。在本文中，我们进一步研究CA可观测性。我们开发了一种方法和一种算法来检验CA可观测性。该方法涉及构建一个增广自动机，其状态是受控系统的当前状态与状态估计的配对。我们证明，K是CA可观测的，当且仅当增广自动机生成的语言等于K。随后开发了一种算法来检验CA可观测性。我们还研究了CA可观测性的性质。我们表明，CA可观测性在（集合）交集下不封闭。注意，（传统）可观测性在交集下是封闭的。我们进一步表明，CA可观测性在并集下不封闭。这与可观测性类似。如果K不是CA可控且CA可观测的，我们提出一种方法来计算一个CA可控且CA可观测的子语言。我们首先计算K的极大CA可控子语言，该子语言可由K的自动机的一个子自动机描述。然后，我们基于该子自动机提出一种基于状态估计的监督器，确保受控系统保持在K内。
英文摘要
In a previous paper, we investigate the control problem of discrete event systems under cyber attacks, where CA-controllability and CA-observability are proposed. We prove that a discrete event system can be controlled to generate a specification language K if and only if K is CA-controllable and CA-observable. While CA controllability can be "converted" to (conventional) controllability, CA-observability cannot be "converted" to (conventional) observability. In this paper, we further investigate CA-observability. We develop a method and an algorithm to check CA-observability. The method involves constructing an augmented automaton whose states are pairs of the current state and state estimate of the supervised system. We prove that K is CA-observable if and only if the language generated by the augmented automaton is equal to K. An algorithm is then developed to check CA-observability. We also investigate the properties of CA-observability. We show that CA-observability is not closed under (set) in tersection. Note that (conventional) observability is closed under intersection. We further show that CA-observability is not closed under union. This is similar to observability. If K is not CA-controllable and CA-observable, we pro pose a method to calculate a CA-controllable and CA observable sublanguage. We first calculate the supremal CA-controllable sublanguage for K which can be described by a sub-automaton of the automaton for K. We then propose a state-estimate-based supervisor based on the subautomaton, which ensures the supervised system stays within K.
