Security Metrics for Uncertain Interconnected Systems under Stealthy Data Injection Attacks

TL;DR

This paper develops a method to quantify the security of interconnected systems against stealthy data injection attacks, providing an upper bound on performance loss using convex optimization, demonstrated on a power grid model.

Contribution

It introduces a convex semi-definite programming approach to bound worst-case performance loss in uncertain interconnected systems under stealthy attacks, considering only input-output channels.

Findings

The method provides a tight upper bound for performance loss.

Numerical simulations validate the approach on a power transmission grid.

The approach accounts for system uncertainties and attack stealthiness.

Abstract

This paper quantifies the security of uncertain interconnected systems under stealthy data injection attacks. In particular, we consider a large-scale system composed of a certain subsystem interconnected with an uncertain subsystem, where only the input-output channels are accessible. An adversary is assumed to inject false data to maximize the performance loss of the certain subsystem while remaining undetected. By abstracting the uncertain subsystem as a class of admissible systems satisfying an $\mathcal{L}_2$ gain constraint, the worst-case performance loss is obtained as the solution to a convex semi-definite program depending only on the certain subsystem dynamics and such an $\mathcal{L}_2$ gain constraint. This solution is proved to serve as an upper bound for the actual worst-case performance loss when the model of the entire system is fully certain. The results are demonstrated through numerical simulations of the power transmission grid spanning Sweden and Northern Denmark.