Data-Driven Resilience Assessment against Sparse Sensor Attacks

We present a data-driven framework for assessing the attack resilience of linear time-invariant systems against malicious false data injection sensor attacks. Based on the concept of sparse observability, data-driven resilience metrics are proposed. First, we derive a data-driven necessary and sufficient condition for assessing the system's resilience against sensor attacks, using data collected without any attacks. If we obtain attack-free data that satisfy a specific rank condition, we can exactly evaluate the attack resilience level even in a model-free setting. We then extend this analysis to a scenario where only poisoned data are available. Given the poisoned data, we can only conservatively assess the system's resilience. In both scenarios, we also provide polynomial-time algorithms to assess the system resilience under specific conditions. Finally, numerical examples illustrate the efficacy and limitations of the proposed framework.