Physical Watermarking for Replay Attack Detection in Continuous-time Systems

TL;DR

This paper investigates physical watermarking for replay attack detection in continuous-time cyber-physical systems, analyzing sampling effects and proposing a method to select sampling periods that balance detection and control performance.

Contribution

It provides a novel analysis of watermarking in sampled-data continuous-time systems and a procedure to choose sampling periods ensuring detectability and control quality.

Findings

Sampling affects detection performance in continuous-time systems.

A procedure for selecting sampling periods is proposed.

Simulations demonstrate the effectiveness of the approach on a quadrotor.

Abstract

Physical watermarking is a well established technique for replay attack detection in cyber-physical systems (CPSs). Most of the watermarking methods proposed in the literature are designed for discrete-time systems. In general, real physical systems evolve in continuous time. In this paper, we analyze the effect of watermarking on sampled-data continuous-time systems controlled via a Zero-Order Hold. We investigate the effect of sampling on detection performance and we provide a procedure to find a suitable sampling period that ensures detectability and acceptable control performance. Simulations on a quadrotor system are used to illustrate the effectiveness of the theoretical results.