Stealthy attacks and attack-resilient interval observers

Industrial control systems have been frequent targets of cyber attacks during the last decade. Adversaries can hinder the safe operation of these systems by tampering with their sensors and actuators, while ensuring that the monitoring systems are not able to detect such attacks in time. This paper presents methods to design and overcome stealthy attacks on linear time-invariant control systems that estimate their state using an interval observer, in the presence of unknown but bounded noise and perturbations. We analyze scenarios in which a malicious agent compromises the sensors and/or the actuators of the system with additive attack signals to steer the state estimate outside of the bounds provided by the interval observer. We first show that maximally disruptive attack sequences that remain undetected by a linear monitor can be computed recursively via linear programming. We then design an attack-resilient interval observer for the system’s state, identifying sufficient conditions on the sensor data for such an observer to be realizable. We propose a computational method to determine optimal observer gains using semi-definite programming and compute bounds for the unknown attack signal as well. In numerical simulations, we illustrate and compare the ability of such interval observers to still provide accurate estimates when under attack.