Delay-Induced Watermarking for Detecting Replay Attacks in Linear Control Systems

Core Concepts

A state-feedback watermarking signal design is proposed to detect replay attacks in linear control systems. The control input is augmented with a random time-delayed term of the system state estimate to secure the system against replay attacks.

Abstract

The paper presents a novel watermarking approach based on random time-delayed state-feedback for detecting replay attacks in linear control systems. The key points are:

The plant is modeled as a discrete-time linear time-invariant (LTI) stochastic system, with a Kalman filter-based state estimator and an LQG controller.

The control input is augmented with a watermarking signal, which is a random time-delayed version of the state estimate. This introduces an additional feedback loop to the control system.

The authors analyze the stability of the closed-loop system with the proposed watermarking approach and derive conditions for exponential convergence of the state to zero.

The impact of the watermarking signal on the system performance is quantified by analyzing the LQG cost function.

The authors develop a theoretical framework for analyzing the detectability of replay attacks using a χ²-based fault detection scheme. They show that the proposed watermarking approach can achieve faster and better detection rates compared to additive Gaussian watermarking.

The effectiveness of the proposed approach is demonstrated through a simulation example of a chemical process control system.

The key contribution is the novel use of random time-delayed state-feedback for watermarking, which offers improved detection capabilities and performance compared to conventional additive Gaussian watermarking schemes.

Stats

The paper does not provide any explicit numerical data or statistics. The key results are presented in the form of theoretical analysis and simulation-based comparisons.

Quotes

There are no direct quotes from the content that are particularly striking or supportive of the key logics.

Key Insights Distilled From

Delay-Induced Watermarking for Detection of Replay Attacks in Linear Systems

by Christoforos... at arxiv.org 04-02-2024

https://arxiv.org/pdf/2404.00850.pdf

Deeper Inquiries

How can the proposed watermarking approach be extended to handle more complex system dynamics, such as nonlinear or time-varying systems

The proposed watermarking approach can be extended to handle more complex system dynamics by incorporating techniques from nonlinear control theory and adaptive control. For nonlinear systems, the state-feedback watermarking signal design can be adapted to include nonlinear state estimators like the Extended Kalman Filter or Unscented Kalman Filter. These filters can handle the nonlinearities present in the system dynamics and provide more accurate state estimates for watermarking. Additionally, techniques from adaptive control can be utilized to adjust the watermarking parameters in real-time based on the system's changing dynamics. This adaptive approach can enhance the robustness of the watermarking scheme against variations in the system behavior.

What are the potential trade-offs between the detection rate and the performance degradation of the controlled system under the proposed watermarking scheme

The trade-offs between the detection rate and the performance degradation of the controlled system under the proposed watermarking scheme are crucial considerations in designing secure control systems. A higher detection rate typically comes at the cost of increased performance degradation, as the watermarking signal introduces additional control inputs that may affect the system's response. By increasing the strength of the watermarking signal to improve detection capabilities, there is a trade-off with the system's overall performance. Balancing these trade-offs involves optimizing the watermarking parameters, such as the feedback gain matrices and the time-delay values, to achieve an acceptable level of detection while minimizing performance degradation.

Can the time-delayed watermarking concept be applied to other types of cyber-attacks beyond replay attacks, such as false data injection or denial-of-service attacks

The concept of time-delayed watermarking can be applied to other types of cyber-attacks beyond replay attacks, such as false data injection or denial-of-service attacks, by modifying the watermarking signal design to target the specific characteristics of these attacks. For false data injection attacks, the watermarking signal can be designed to detect anomalies in the sensor measurements that deviate from the expected behavior. By incorporating anomaly detection algorithms into the watermarking scheme, the system can identify and mitigate the effects of false data injection attacks. Similarly, for denial-of-service attacks, the watermarking signal can be tailored to detect disruptions in the control inputs or communication channels, enabling the system to respond effectively to such attacks. The key lies in customizing the watermarking approach to address the unique challenges posed by different types of cyber-attacks.