On model‐based detectors for linear time‐invariant stochastic systems under sensor attacks

A vector‐valued model‐based cumulative sum (CUSUM) procedure is proposed for identifying faulty/falsified sensor measurements. First, given the system dynamics, the authors derive tools for tuning the CUSUM procedure in the fault/attack‐free case to fulfil the desired detection performance (in terms of false alarm rate). They use the widely‐used chi‐squared fault/attack detection procedure as a benchmark to compare the performance of the CUSUM. In particular, they characterise the state degradation that a class of attacks can induce the system while enforcing that the detectors (CUSUM and chi‐squared) do not raise alarms. In doing so, they find the upper bound of state degradation that is possible by an undetected attacker. They quantify the advantage of using a dynamic detector (CUSUM), which leverages the history of the state, over a static detector (chi‐squared), which uses a single measurement at a time. Simulations of a chemical reactor with a heat exchanger are presented to illustrate the performance of their tools.