Minimum Robust Invariant Sets and Kalman Filtering in Cyber Attacking and Defending

The paper provides a data integrity cyber-attack detection framework based on minimum robust positively invariant sets. A general linear control system with a Kalman filter is considered. The set localization of the state estimator error is taken into account for developing the attack detector. An intelligent attacker algorithm is developed that has access to a subset of signals from the sensor and actuator channel of the control system. It is assumed that the attacker possesses the entire control system model to perform the most proficient attack for a certain set-up of data availability and compromisation. The attacker compromises a set of measurement data under the constraint of remaining non-discovered by the detector. The presented methodology allows assessing the effectiveness of the control system defense achievable in various data integrity attack scenarios. The developed detector and attacker algorithm were implemented on an illustrative example of a power system with two control areas and automatic generation control.