Selection of a stealthy and harmful attack function in discrete event systems

In this paper we consider the problem of joint state estimation under attack in partially-observed discrete event systems. An operator observes the evolution of the plant to evaluate its current states. The attacker may tamper with the sensor readings received by the operator inserting dummy events or erasing real events that have occurred in the plant with the goal of preventing the operator from computing the correct state estimation. An attack function is said to be harmful if the state estimation consistent with the correct observation and the state estimation consistent with the corrupted observation satisfy a given misleading relation. On the basis of an automaton called joint estimator, we show how to compute a supremal stealthy joint subestimator that allows the attacker to remain stealthy, no matter what the future evolution of the plant is. Finally, we show how to select a stealthy and harmful attack function based on such a subestimator.