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Risk Assessment for Nonlinear Cyber-Physical Systems under Stealth Attacks

Guang Chen, Zhicong Sun, Yulong Ding, Shuang-hua Yang

TL;DR

This work proposes a framework that considers both the reachability of a system and the risk distribution of a scenario under stealth attacks, and introduces a metric to dynamically quantify the risk.

Abstract

Stealth attacks pose potential risks to cyber-physical systems because they are difficult to detect. Assessing the risk of systems under stealth attacks remains an open challenge, especially in nonlinear systems. To comprehensively quantify these risks, we propose a framework that considers both the reachability of a system and the risk distribution of a scenario. We propose an algorithm to approximate the reachability of a nonlinear system under stealth attacks with a union of standard sets. Meanwhile, we present a method to construct a risk field to formally describe the risk distribution in a given scenario. The intersection relationships of system reachability and risk regions in the risk field indicate that attackers can cause corresponding risks without being detected. Based on this, we introduce a metric to dynamically quantify the risk. Compared to traditional methods, our framework predicts the risk value in an explainable way and provides early warnings for safety control. We demonstrate the effectiveness of our framework through a case study of an automated warehouse.

Risk Assessment for Nonlinear Cyber-Physical Systems under Stealth Attacks

TL;DR

This work proposes a framework that considers both the reachability of a system and the risk distribution of a scenario under stealth attacks, and introduces a metric to dynamically quantify the risk.

Abstract

Stealth attacks pose potential risks to cyber-physical systems because they are difficult to detect. Assessing the risk of systems under stealth attacks remains an open challenge, especially in nonlinear systems. To comprehensively quantify these risks, we propose a framework that considers both the reachability of a system and the risk distribution of a scenario. We propose an algorithm to approximate the reachability of a nonlinear system under stealth attacks with a union of standard sets. Meanwhile, we present a method to construct a risk field to formally describe the risk distribution in a given scenario. The intersection relationships of system reachability and risk regions in the risk field indicate that attackers can cause corresponding risks without being detected. Based on this, we introduce a metric to dynamically quantify the risk. Compared to traditional methods, our framework predicts the risk value in an explainable way and provides early warnings for safety control. We demonstrate the effectiveness of our framework through a case study of an automated warehouse.
Paper Structure (25 sections, 7 theorems, 53 equations, 7 figures, 2 algorithms)

This paper contains 25 sections, 7 theorems, 53 equations, 7 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Control system
  4. state estimation
  5. Detection
  6. The system under stealth attacks
  7. Reachability Analysis
  8. Preliminaries
  9. Set representation
  10. Over-approximation
  11. Reachability analysis
  12. Algorithm overview
  13. Step 1: Initialization
  14. Step 2: UKF update
  15. Step 3: System update
  16. ...and 10 more sections

Key Result

Lemma 1

For any two Taylor models $<p_1, \mathbf{I}_1>_{TM}$ and $<p_2,\mathbf{I}_2>_{TM}$ over the same domain $\mathbf{X}$, the operation of sum and product between them can be easily computed by where $<p_3, \mathbf{I}_3>_{TM}=p_{\frac{1}{x}}(p_2(\mathbf{X})\oplus\mathbf{I}_2)\oplus\mathsf{Int}(r_{\frac{1}{x}}(p_2(\mathbf{X})\oplus\mathbf{I}_2))$.

Figures (7)

  • Figure 1: The framework to assess the risk of systems under stealth attacks.
  • Figure 2: An attacked system architecture: by injecting false data into the measurements, an attacker can intrude into the system without being detected.
  • Figure 3: Algorithm overview: After initialization, we iterate and approximate the state set, and take the union of the approximated state sets as the approximation of the ASR set.
  • Figure 4: An event occurrence with a given probability $\gamma$ when the system state is in the critical region.
  • Figure 5: RR metric: Quantifying the risk value based on ASR set approximation and the risk field.
  • ...and 2 more figures

Theorems & Definitions (16)

  • Definition 1: Zonotope
  • Definition 2: Taylor model
  • Lemma 1: Taylor model arithmetic
  • Proof 1
  • Proposition 1: Zonotope to TM
  • Proof 2
  • Proposition 2: Ellipsoid to Taylor model
  • Proof 3
  • Definition 3: ASR set
  • Theorem 1
  • ...and 6 more