Stealthy actuator signal attacks in stochastic control systems : performance and limitations

In this technical note, the trade-off between the attack detectability and the performance degradation in stochastic cyber-physical systems is investigated. We consider a linear time-invariant system in which the attack detector performs a hypothesis test on the state estimation residual of the Kalman filter to detect malicious tampering with the actuator signals. We adopt a notion of attack stealthiness to quantify the degree of stealth by limiting the maximum achievable exponents of both false alarm rate and detection probability below certain thresholds. And conditions for an arbitrary actuator attack to have a specific level of stealthiness are derived. Additionally, we characterize the upper bound of the performance degradation induced by attackers with a given extent of stealthiness and design the attack that achieves the stated upper bound in right-invertible systems. Finally, our results are illustrated via numerical examples.