Quickest Detection of Deception Attacks in Networked Control Systems with Physical Watermarking

TL;DR

This paper introduces a novel attack detection method for networked control systems using physical watermarking and CUSUM tests, providing theoretical analysis and design insights to optimize detection delay and system security.

Contribution

It develops a new quickest detection scheme with analytical expressions for detection delay in MIMO systems, and offers design guidelines for optimal watermarking signals.

Findings

Detection delay inversely related to Kullback-Leibler divergence

Optimal watermarking enhances attack detectability

Simulation results validate theoretical analysis

Abstract

In this paper, we propose and analyze an attack detection scheme for securing the physical layer of a networked control system against attacks where the adversary replaces the true observations with stationary false data. An independent and identically distributed watermarking signal is added to the optimal linear quadratic Gaussian (LQG) control inputs, and a cumulative sum (CUSUM) test is carried out using the joint distribution of the innovation signal and the watermarking signal for quickest attack detection. We derive the expressions of the supremum of the average detection delay (SADD) for a multi-input and multi-output (MIMO) system under the optimal and sub-optimal CUSUM tests. The SADD is asymptotically inversely proportional to the expected Kullback-Leibler divergence (KLD) under certain conditions. The expressions for the MIMO case are simplified for multi-input and single-output systems and explored further to distil design insights. We provide insights into the design of an optimal watermarking signal to maximize KLD for a given fixed increase in LQG control cost when there is no attack. Furthermore, we investigate how the attacker and the control system designer can accomplish their respective objectives by changing the relative power of the attack signal and the watermarking signal. Simulations and numerical studies are carried out to validate the theoretical results.