Quickest physical watermarking-based detection of measurement replacement attacks in networked control systems

In this paper, we propose and analyze an attack detection scheme for securing the physical layer of a net-worked control system (NCS) with a wireless sensor network against attacks where the adversary replaces the true observations with stationary false data. An independent and identically distributed watermark-ing 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 detec-tion 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 diver-gence (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 de-signer 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.(c) 2023 The Author(s). Published by Elsevier Ltd on behalf of European Control Association. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )