Quickest Detection of Deception Attacks on Cyber-Physical Systems with a Parsimonious Watermarking Policy

TL;DR

This paper develops an optimal watermarking policy for cyber-physical systems to quickly detect deception attacks while minimizing control costs, using stochastic control and sequential detection theory.

Contribution

It introduces a two-threshold policy based on Shiryaev statistics to optimally balance detection speed and control cost in attack detection.

Findings

Optimal watermarking reduces detection delay effectively.

Derived approximate formulas for detection delay and false alarm rate.

Simulation validates the theoretical optimal policy.

Abstract

The addition of a physical watermarking signal to the control input increases the detection probability of data deception attacks at the expense of increased control cost. In this paper, we propose a parsimonious policy to reduce the average number of watermarking events when the attack is not present, which in turn reduces the control cost. We model the system as a stochastic optimal control problem and apply the dynamic programming to minimize the average detection delay (ADD) for fixed upper bounds on false alarm rate (FAR) and increased control cost. The optimal solution results in a two threshold policy on the posterior probability of attack, which is derived from the Shiryaev statistics for sequential change detection assuming the change point is a random variable with a geometric distribution. We derive approximate expressions of ADD and FAR applying the non-linear renewal theory. The relationship between the average number of watermarking added before the attack and the increase in control cost is also derived. We design the optimal watermarking that maximizes the Kullback-Leibler divergence for a fixed increase in the control cost. Simulation studies are performed to illustrate and validate the theoretical results.