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CUSUM and chi-squared attack detection of compromised sensors

A vector-valued model-based cumulative sum (CUSUM) procedure is proposed for identifying falsified sensor measurements. To fulfill a desired detection performance, given the system dynamics, we derive tools for tuning the CUSUM procedure. We characterize the state degradation that a stealthy attacker can induce to the system while remaining undetected by the detection procedure. We 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. Simulation experiments are presented to illustrate the performance of the detection scheme.