Security in stochastic control systems: Fundamental limitations and performance bounds

This work proposes a novel metric to characterize the resilience of stochastic cyber-physical systems to attacks and faults. We consider a single-input single-output plant regulated by a control law based on the estimate of a Kalman filter. We allow for the presence of an attacker able to hijack and replace the control signal. The objective of the attacker is to maximize the estimation error of the Kalman filter - which in turn quantifies the degradation of the control performance - by tampering with the control input, while remaining undetected. We introduce a notion of ε-stealthiness to quantify the difficulty to detect an attack when an arbitrary detection algorithm is implemented by the controller. For a desired value of ε-stealthiness, we quantify the largest estimation error that an attacker can induce, and we analytically characterize an optimal attack strategy. Because our bounds are independent of the detection mechanism implemented by the controller, our information-theoretic analysis characterizes fundamental security limitations of stochastic cyber-physical systems.