  A vector-valued model-based cumulative sum (CUSUM) procedure is proposed for
identifying faulty/falsified sensor measurements. First, given the system
dynamics, we derive tools for tuning the CUSUM procedure in the fault/attack
free case to fulfill a desired detection performance (in terms of false alarm
rate). We use the widely-used chi-squared fault/attack detection procedure as a
benchmark to compare the performance of the CUSUM. In particular, we
characterize the state degradation that a class of attacks can induce to the
system while enforcing that the detectors (CUSUM and chi-squared) do not raise
alarms. In doing so, we find the upper bound of state degradation that is
possible by an undetected attacker. 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.
Simulations of a chemical reactor with heat exchanger are presented to
illustrate the performance of our tools.
