State estimation under attack in partially-observed discrete event systems

The problem of state estimation in the setting of partially-observed discrete event systems subject to cyber attacks is considered. An operator observes a plant through a natural projection that hides the occurrence of certain events. The objective of the operator is that of estimating the current state of the system. The observation is corrupted by an attacker which can insert and erase some sensor readings with the aim of altering the state estimation of the operator. Furthermore, the attacker wants to remain stealthy, namely the operator should not realize that its observation has been corrupted. An automaton, called attack structure, is defined to describe the set of all possible attacks. In more details, first, an unbounded attack structure is obtained by concurrent composition of two state observers, the attacker observer and the operator observer. Then, the attack structure is refined to obtain a supremal stealthy attack substructure. An attack function may be selected from the supremal stealthy attack substructure and it is said harmful when some malicious goal of the attacker is reached, namely if the set of states consistent with the observation produced by the system and the set of states consistent with the corrupted observation belong to a given relation. The proposed approach can be dually used to verify if there exists a harmful attack for the given system: this allows one to establish if the system is safe under attack.