False Data-Injection Attack Detection in Cyber-Physical Systems: A Wasserstein Distributionally Robust Reachability Optimization Approach

TL;DR

This paper introduces a distributionally robust approach using Wasserstein ambiguity sets to design anomaly detectors for cyber-physical systems, effectively handling unknown disturbance distributions and stealthy false-data injection attacks.

Contribution

It proposes a new security metric based on asymptotic reachability analysis and formulates a robust detector design as a semi-infinite DRO problem with an effective solution algorithm.

Findings

The approach effectively detects FDI attacks under unknown disturbances.

The method balances robustness and false alarm rate.

Case study shows improved robustness against unknown distributions.

Abstract

Cyber-physical system (CPS) is the foundational backbone of modern critical infrastructures, so ensuring its security and resilience against cyber-attacks is of pivotal importance. This paper addresses the challenge of designing anomaly detectors for CPS under false-data injection (FDI) attacks and stochastic disturbances governed by unknown probability distribution. By using the Wasserstein ambiguity set, a prevalent data-driven tool in distributionally robust optimization (DRO), we first propose a new security metric to deal with the absence of disturbance distribution. This metric is designed by asymptotic reachability analysis of state deviations caused by stealthy FDI attacks and disturbance in a distributionally robust confidence set. We then formulate the detector design as a DRO problem that optimizes this security metric while controlling the false alarm rate robustly under a set of distributions. This yields a trade-off between robustness to disturbance and performance degradation under stealthy attacks. The resulting design problem turns out to be a challenging semi-infinite program due to the existence of distributionally robust chance constraints. We derive its exact albeit non-convex reformulation and develop an effective solution algorithm based on sequential minimization. Finally, a case study on a simulated three-tank is illustrated to demonstrate the efficiency of our design in robustifying against unknown disturbance distribution.