State estimation for discrete-event systems with reliable states under sequential attacks

Cyber–physical systems are crucial in industry and are often modeled as discrete-event systems for analysis. One major concern is that the communication in cyber–physical systems is susceptible to three types of attacks: deletions, insertions, and substitutions. To prevent communication signals from being tampered with, communication protection can be used in particular states referred to as reliable states. In this paper, the state estimation problem for discrete-event systems with reliable states under sequential attacks is formulated and solved. Additionally, under sequential attacks, we construct a tampered reliable automaton, derived from the original system, to achieve state estimation efficiently. Finally, we analyze the impact of reliable states on the opacity of the tampered reliable automaton when an original automaton is opaque.