基于加权自动机的离散事件系统的不透明性和可诊断性研究

在离散事件系统中，不透明性和可诊断性是两个被广泛研究的重要热点问题。不透明性是一种机密性属性，它捕获是否可以向入侵者透露系统的秘密。可诊断性要求任何故障的发生可以在有限的延迟内被检测到。本项目研究由加权自动机建模的时间离散事件系统的不透明性和可诊断性验证问题。在不透明性框架下，研究加权自动机的当前状态不透明性和初始状态不透明性。通过构建观测器和初始状态观测器，给出当前状态不透明性和初始状态不透明性的判据；在可诊断性框架下，研究加权自动机的K-可诊断性和T-可诊断性。通过构建诊断器和验证器，给出不同计算复杂度的K-可诊断性判据；探讨T-可诊断性和K-可诊断性之间的关系；对于可诊断的系统，用代数方法确定故障被检测到所需要的最大时间。本项目补充和完善离散事件系统不透明性和可诊断性的研究，并为许多实际系统的不透明性和可诊断性判定提供重要的理论依据。

In discrete event systems, opacity and diagnosability are two significant hot issues that have been widely studied. Opacity is a confidentiality property that captures whether the secrets of a system can be disclosed to an intruder. Diagnosability requires that the occurrence of any fault can be detected within a finite delay. This project studies the opacity and diagnosability verification problems for time discrete event systems modeled by weighted automata. Under the framework of opacity, the current-state opacity and initial-state opacity for weighted automata are studied. By constructing an observer and an initial-state observer, the criteria for verifying the current-state opacity and initial-state opacity of a weighted automaton are given. Under the framework of diagnosability, the K-diagnosability and T-diagnosability for weighted automata are studied. By constructing a diagnoser and a verifier, the criteria for checking K-diagnosability of different computational complexity are given. The relationship between T-diagnosability and K-diagnosability is explored. For a K-diagnosable system, the maximum time required for any fault to be detected is determined using an algebraic approach. This project supplements and improves the research on opacity and diagnosability for discrete event systems, and provides an important theoretical basis for determining the opacity and diagnosability of many real-world systems.