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Detection and Identification of Sensor Attacks Using Data

Takumi Shinohara, Karl H. Johansson, Henrik Sandberg

TL;DR

The paper tackles detecting and identifying sensor attacks from data alone in a model-free setting, where outputs may be malicious and system matrices are unknown. It develops two data-driven frameworks: (1) under known $l$-sparse observability, it leverages rank tests on Hankel-type data matrices to detect and pinpoint attacked sensors; (2) with partially clean output data, it exploits a clean interval and minimum excitability horizon to achieve detection/identification via rank and SVD-based residuals. Theoretical results provide sufficient rank conditions and constructive algorithms, validated by simulations on a three-inertia system showing success where ROBPCA fails. The work advances data-driven secure state estimation by enabling detection and removal of compromised data to enable subsequent control tasks.

Abstract

In this paper, we investigate data-driven attack detection and identification in a model-free setting. Unlike existing studies, we consider the case where the available output data include malicious false-data injections. We aim to detect and identify such attacks solely from the compromised data. We address this problem in two scenarios: (1) when the system operator is aware of the system's sparse observability condition, and (2) when the data are partially clean (i.e., attack-free). In both scenarios, we derive conditions and algorithms for detecting and identifying attacks using only the compromised data. Finally, we demonstrate the effectiveness of the proposed framework via numerical simulations on a three-inertia system.

Detection and Identification of Sensor Attacks Using Data

TL;DR

The paper tackles detecting and identifying sensor attacks from data alone in a model-free setting, where outputs may be malicious and system matrices are unknown. It develops two data-driven frameworks: (1) under known -sparse observability, it leverages rank tests on Hankel-type data matrices to detect and pinpoint attacked sensors; (2) with partially clean output data, it exploits a clean interval and minimum excitability horizon to achieve detection/identification via rank and SVD-based residuals. Theoretical results provide sufficient rank conditions and constructive algorithms, validated by simulations on a three-inertia system showing success where ROBPCA fails. The work advances data-driven secure state estimation by enabling detection and removal of compromised data to enable subsequent control tasks.

Abstract

In this paper, we investigate data-driven attack detection and identification in a model-free setting. Unlike existing studies, we consider the case where the available output data include malicious false-data injections. We aim to detect and identify such attacks solely from the compromised data. We address this problem in two scenarios: (1) when the system operator is aware of the system's sparse observability condition, and (2) when the data are partially clean (i.e., attack-free). In both scenarios, we derive conditions and algorithms for detecting and identifying attacks using only the compromised data. Finally, we demonstrate the effectiveness of the proposed framework via numerical simulations on a three-inertia system.

Paper Structure

This paper contains 19 sections, 7 theorems, 59 equations, 12 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work and Motivation
  3. Contributions
  4. Problem Formulation
  5. System Model and Problem of Interest
  6. Data Representation
  7. Undetectable Attacks and Sparse Observability
  8. Data-Driven Attack Detection and Identification under Sparse Observability Conditions
  9. Data-Driven Attack Detection and Identification with Partially Clean Output Data
  10. Attack Detection
  11. Attack Identification
  12. Numerical Simulations
  13. Simulation Setting
  14. Benchmark: ROBPCA
  15. Results
  16. ...and 4 more sections

Key Result

Theorem 1

Suppose Assumptions assumption:operator and assumption:attacker hold, the input $u^{[N-1]}$ is persistently exciting of order $q \geq n$, and $N -q +1 \geq mq + n$. Further, assume that the system is $l$-sparse observable. Then, the following statements are true:

Figures (12)

  • Figure 1: Relationship between $U^q$ and $\tilde{U}^{(q,T)}_{(k)}$. The same applies to $Y$, $\Lambda$, and $Z$.
  • Figure 2: Graphical explanation of $\Lambda^q$ and $\tilde{\Lambda}^{(q,T)}_{(k)}$ considering the attack-free interval $\mathcal{K}_0$, where the gray-shaded elements are all zero and the clean, transition, and attack intervals are illustrated in the vector sense.
  • Figure 3: Input data of three-inertia system.
  • Figure 4: No attack case.
  • Figure 5: Attack sequence of (\ref{['eq:simulation_attack']}).
  • ...and 7 more figures

Theorems & Definitions (22)

  • Definition 1: Undetectable Attacks
  • Definition 2: Sparse Observability
  • Theorem 1
  • proof
  • Remark 1
  • Remark 2
  • Definition 3: Minimum Excitability Horizon Length
  • Theorem 2
  • proof
  • Remark 3
  • ...and 12 more