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

In this technical note, the tradeoff 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 innovation 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 probability and detection probability below certain thresholds. And the conditions for any actuator attack to have a specific level of stealthiness are derived. Additionally, we characterize the upper bound of the performance degradation induced by attacks with a given extent of stealthiness that produces independent and identically distributed Gaussian innovations, and design the attack, which achieves the stated upper bound for right-invertible systems. Finally, our results are illustrated via numerical examples.