Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Data-driven Control Against False Data Injection Attacks

Wenjie Liu, Lidong Li, Jian Sun, Fang Deng, Gang Wang, Jie Chen

TL;DR

The paper addresses stabilizing unknown linear systems under actuator FDI attacks by modeling the problem as a switched linear system and leveraging a data-driven approach that fuses offline healthy-data information with online attacked-data observations. It introduces two on-the-fly SDPs to compute a time-varying gain $K(t)$ that stabilizes all data-consistent subsystems, ensuring recursive feasibility and exponential stability under mild attack energy bounds $ar{oldsymbol{ u}}$. The key contributions are a general FDI attack model with switching constraints, a data-driven procedure to construct a minimum-volume matrix ellipsoid intersecting with the attack-bound set, and theoretical guarantees of stability and bounded controller gain, complemented by two numerical examples (Power Generator and Aircraft Engine) validating effectiveness and performance trade-offs. This framework provides a practical, model-free route to resilient CPS control against sophisticated FDI threats with uncertain system dynamics.

Abstract

The rise of cyber-security concerns has brought significant attention to the analysis and design of cyber-physical systems (CPSs). Among the various types of cyberattacks, denial-of-service (DoS) attacks and false data injection (FDI) attacks can be easily launched and have become prominent threats. While resilient control against DoS attacks has received substantial research efforts, countermeasures developed against FDI attacks have been relatively limited, particularly when explicit system models are not available. To address this gap, the present paper focuses on the design of data-driven controllers for unknown linear systems subject to FDI attacks on the actuators, utilizing input-state data. To this end, a general FDI attack model is presented, which imposes minimally constraints on the switching frequency of attack channels and the magnitude of attack matrices. A dynamic state feedback control law is designed based on offline and online input-state data, which adapts to the channel switching of FDI attacks. This is achieved by solving two data-based semi-definite programs (SDPs) on-the-fly to yield a tight approximation of the set of subsystems consistent with both offline clean data and online attack-corrupted data. It is shown that under mild conditions on the attack, the proposed SDPs are recursively feasible and controller achieves exponential stability. Numerical examples showcase its effectiveness in mitigating the impact of FDI attacks.

Data-driven Control Against False Data Injection Attacks

TL;DR

The paper addresses stabilizing unknown linear systems under actuator FDI attacks by modeling the problem as a switched linear system and leveraging a data-driven approach that fuses offline healthy-data information with online attacked-data observations. It introduces two on-the-fly SDPs to compute a time-varying gain that stabilizes all data-consistent subsystems, ensuring recursive feasibility and exponential stability under mild attack energy bounds . The key contributions are a general FDI attack model with switching constraints, a data-driven procedure to construct a minimum-volume matrix ellipsoid intersecting with the attack-bound set, and theoretical guarantees of stability and bounded controller gain, complemented by two numerical examples (Power Generator and Aircraft Engine) validating effectiveness and performance trade-offs. This framework provides a practical, model-free route to resilient CPS control against sophisticated FDI threats with uncertain system dynamics.

Abstract

The rise of cyber-security concerns has brought significant attention to the analysis and design of cyber-physical systems (CPSs). Among the various types of cyberattacks, denial-of-service (DoS) attacks and false data injection (FDI) attacks can be easily launched and have become prominent threats. While resilient control against DoS attacks has received substantial research efforts, countermeasures developed against FDI attacks have been relatively limited, particularly when explicit system models are not available. To address this gap, the present paper focuses on the design of data-driven controllers for unknown linear systems subject to FDI attacks on the actuators, utilizing input-state data. To this end, a general FDI attack model is presented, which imposes minimally constraints on the switching frequency of attack channels and the magnitude of attack matrices. A dynamic state feedback control law is designed based on offline and online input-state data, which adapts to the channel switching of FDI attacks. This is achieved by solving two data-based semi-definite programs (SDPs) on-the-fly to yield a tight approximation of the set of subsystems consistent with both offline clean data and online attack-corrupted data. It is shown that under mild conditions on the attack, the proposed SDPs are recursively feasible and controller achieves exponential stability. Numerical examples showcase its effectiveness in mitigating the impact of FDI attacks.
Paper Structure (12 sections, 2 theorems, 40 equations, 6 figures, 1 algorithm)

This paper contains 12 sections, 2 theorems, 40 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Formulation
  3. Healthy System
  4. Switched FDI Attack
  5. System Remodeling and Problem Formulation
  6. Data-driven Control Against FDI
  7. Data-driven Control Strategy
  8. Theoretical Guarantees
  9. Numerical Examples
  10. Power Generator
  11. Aircraft Engine System
  12. Conclusions

Key Result

Theorem 3.1

Under Assumptions as:1:co---as:5:ctrl, let $U_0$, $X_0$ and $X_1$ be given in eq:X0. Consider arbitrary initial conditions $x_p(0)$ and $u_o(0)$ for the system eq:sys with Algorithm alg:ctrl. There exist constants $\bar{\delta} >0$ and $\underline{\epsilon}_1 \in (0,1)$ such that for all $\delta \in

Figures (6)

  • Figure 1: System \ref{['eq:sys']} under FDI attacks on actuators.
  • Figure 2: Sets $\mathcal{B}^{\delta}$ (red solid circle), $\mathcal{E}_t$ (green solid ellipsoid), and $\mathcal{I}^*_t$ (blue dashed-line ellipsoid) for a first-order system.
  • Figure 3: System performance for Section \ref{['sec:num:1']}. Top: System trajectories under the proposed resilient controller and the ID-based method in wu2019optimalswitching; Bottom: Switching times of attacks.
  • Figure 4: System's performances under different $\epsilon_1$ and $\epsilon_2$.
  • Figure 5: System's performance for Section \ref{['sec:num:2']}. Panels (a)--(c): state trajectories under the proposed Alg. \ref{['alg:ctrl']} (+ marked dotted line), data-driven method in rotulo2021online (solid line), and time-invariant controller (dashed line); Panel (d): Switching times.
  • ...and 1 more figures

Theorems & Definitions (9)

  • Definition 1.1: Persistence of excitation
  • Example 2.1
  • Remark 3.1: $Z_t$ vs. $Z_{\sigma(t-1)}$
  • Example 3.1
  • Theorem 3.1
  • Remark 3.2: Complexity
  • Remark 3.3: Noisy data
  • Remark 3.4: Parameters $\epsilon_1$ and $\epsilon_2$
  • Theorem 3.2