Active Opacity of Fuzzy Discrete Event Systems

In recent years, the research on opacity of discrete event systems has attracted widespread attention due to the successful application of opacity in information security of cyber-physical systems. In this research, the enforcement issue of the current state opacity is investigated under the framework of fuzzy discrete event systems modeled by fuzzy automata. The notion of active opacity of fuzzy systems is formalized. For a fuzzy system that does not possess current state opacity, an active control strategy is introduced and then an approach to active opacity is proposed. By constructing a controllability verifier of fuzzy secret states, a controllable event sequence is identified for each secret state, which reinforces the opacity of the fuzzy system by allowing the system to enter a secret state undetected by intruders. Based on the controllability verifier, the necessary and sufficient condition for the active opacity of fuzzy systems is presented, and a corresponding verification algorithm is proposed.