Set-Based Anomaly Detector and Stealthy Attack Impact using Constrained Zonotopes

In this paper, a set-based detector is developed and analyzed based on the propagation of nominal (no attacks), actual (possibly with attacks), and perceived (corrupted by attacks) residuals due to bounded system and measurement noise uncertainties. The set of stealthy attacks (attacks that raise no alarms) is characterized and the impact of these stealthy attacks on the system state is quantified. When implemented through the set tools of constrained zonotopes, this approach provides accurate, time-varying attack-reachable sets that can be used to evaluate the safety and performance of systems in adversarial conditions. These tools are demonstrated through two case studies.