Data-Driven Resilience Assessment against Sparse Sensor Attacks

Abstract

We develop a data-driven framework for assessing the resilience of linear time-invariant systems against malicious false-data-injection sensor attacks. Leveraging sparse observability, we propose data-driven resilience metrics and derive necessary and sufficient conditions for two data-availability scenarios. For attack-free data, we show that when a rank condition holds, the resilience level can be computed exactly from the data alone, without prior knowledge of the system parameters. We then extend the analysis to the case where only poisoned data are available and show that the resulting assessment is necessarily conservative. For both scenarios, we provide algorithms for computing the proposed metrics and show that they can be computed in polynomial time under an additional spectral condition. A numerical example illustrates the efficacy and limitations of the proposed framework.

Figures (2)

• Figure 1: Illustration of data informativity for $\delta$-sparse observability. In this illustration, the true but unknown system $(\bar{A},\bar{C})$ is $8$-sparse observable, i.e., $\delta^{\max} = 8$. On the other hand, the data are informative for $7$-sparse observability, i.e., $\varrho^{\max} = 7$, because the data-consistent systems are $7$-sparse observable. Thus, in this illustration, $\varrho^{\max} < \delta^{\max}$.
• Figure 2: Simulation results for the pendulum system.

Theorems & Definitions (16)

• Definition 1: Sparse Observability
• Proposition 1
• proof
• Definition 2
• Lemma 1
• proof
• Theorem 1
• proof
• Corollary 1
• proof