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Process Resilience under Optimal Data Injection Attacks

Xiuzhen Ye, Wentao Tang

TL;DR

The paper develops an information-theoretic framework to study process resilience under optimal data injection attacks (DIAs) on linear stochastic systems. Attacks are modeled as Gaussian injections that maximize disruption of the stationary joint distribution of states and estimates while minimizing detection likelihood, governed by a tunable weight $\lambda$. It provides analytical results for full attacks (including convexity conditions and a Lyapunov-type solution) and a practical greedy algorithm for $k$-sparse attacks, with numerical validation on a two-CSTR plant showing sensor-level vulnerability patterns and Pareto tradeoffs between disruption and stealth. The work offers a principled basis for assessing and improving sensor resilience in cyber-physical processes, while highlighting assumptions (linearity, full-knowledge) and avenues for extending to nonlinear and partial-knowledge settings.

Abstract

In this paper, we study the resilience of process systems in an {\it information-theoretic framework}, from the perspective of an attacker capable of optimally constructing data injection attacks. The attack aims to distract the stationary distributions of process variables and stay stealthy, simultaneously. The problem is formulated as designing a multivariate Gaussian distribution to maximize the Kullback-Leibler divergence between the stationary distributions of states and state estimates under attacks and without attacks, while minimizing that between the distributions of sensor measurements. When the attacker has limited access to sensors, sparse attacks are proposed by incorporating a sparsity constraint. {We conduct theoretical analysis on the convexity of the attack construction problem and present a greedy algorithm, which enables systematic assessment of measurement vulnerability, thereby offering insights into the inherent resilience of process systems. We numerically evaluate the performance of proposed constructions on a two-reactor process.

Process Resilience under Optimal Data Injection Attacks

TL;DR

The paper develops an information-theoretic framework to study process resilience under optimal data injection attacks (DIAs) on linear stochastic systems. Attacks are modeled as Gaussian injections that maximize disruption of the stationary joint distribution of states and estimates while minimizing detection likelihood, governed by a tunable weight . It provides analytical results for full attacks (including convexity conditions and a Lyapunov-type solution) and a practical greedy algorithm for -sparse attacks, with numerical validation on a two-CSTR plant showing sensor-level vulnerability patterns and Pareto tradeoffs between disruption and stealth. The work offers a principled basis for assessing and improving sensor resilience in cyber-physical processes, while highlighting assumptions (linearity, full-knowledge) and avenues for extending to nonlinear and partial-knowledge settings.

Abstract

In this paper, we study the resilience of process systems in an {\it information-theoretic framework}, from the perspective of an attacker capable of optimally constructing data injection attacks. The attack aims to distract the stationary distributions of process variables and stay stealthy, simultaneously. The problem is formulated as designing a multivariate Gaussian distribution to maximize the Kullback-Leibler divergence between the stationary distributions of states and state estimates under attacks and without attacks, while minimizing that between the distributions of sensor measurements. When the attacker has limited access to sensors, sparse attacks are proposed by incorporating a sparsity constraint. {We conduct theoretical analysis on the convexity of the attack construction problem and present a greedy algorithm, which enables systematic assessment of measurement vulnerability, thereby offering insights into the inherent resilience of process systems. We numerically evaluate the performance of proposed constructions on a two-reactor process.

Paper Structure

This paper contains 16 sections, 6 theorems, 46 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Dynamical Model and Attack
  4. Attack Detection
  5. Information-theoretic attacks
  6. Information-Theoretic Measure
  7. Attack Constructions
  8. Full attack
  9. Sparse Attack
  10. Optimal Single Measurement Attacks
  11. $k$-sparse Attacks
  12. Numerical Case Study and Vulnerability Analysis
  13. Performance of Single Measurement Attacks
  14. Performance of $k$-sparse Attacks
  15. Discussion on Vulnerability and Resilience
  16. ...and 1 more sections

Key Result

Proposition 1

The multivariate Gaussian attack construction ${\bf a} \sim {\cal N} ( \hbox{\boldmath$\mu$}_a, \hbox{\boldmath$\Sigma$}_{{\bf a} {\bf a}} )$ that jointly maximizes the disruption captured by $D(P_{\hbox{\boldmath$\xi$}_a} \| P_{\hbox{\boldmath$\xi$}})$ and minimizes the probability of detection cha with $\textnormal{0}$ being a zero matrix with dimension $n$ by $n$ and the matrices ${\bf M}_1$ an

Figures (5)

  • Figure 1: Information-theoretic framework for DIA construction on control systems.
  • Figure 2: Attack performance of single measurement attacks in terms of $\lambda$ with full knowledge and incomplete knowledge of second-order statistics.
  • Figure 3: Analysis of single measurement attacks in terms of stationary distributions.
  • Figure 4: Analysis of $k$-sparse attacks.
  • Figure 5: Analysis of $k$-sparse attack in terms of stationary distributions.

Theorems & Definitions (6)

  • Proposition 1
  • Proposition 2
  • Theorem 1
  • Theorem 2
  • Lemma 1
  • Theorem 3