On the Computation of Worst Attacks: a LP Framework

TL;DR

This paper develops a linear programming framework to compute worst-case stealthy false data injection attacks on LTI systems and proposes a controller synthesis method to mitigate their impact.

Contribution

It introduces a tractable LP-based approach for designing worst stealthy attacks and a method for controller synthesis to minimize attack impact.

Findings

LP framework effectively computes worst attacks

Method enables systematic attack design and mitigation

Provides necessary and sufficient conditions for stealthy attacks

Abstract

We consider the problem of false data injection attacks modeled as additive disturbances in various parts of a general LTI feedback system and derive necessary and sufficient conditions for the existence of stealthy unbounded attacks. We also consider the problem of characterizing the worst, bounded and stealthy attacks. This problem involves a maximization of a convex function subject to convex constraints, and hence, in principle, it is not easy to solve. However, by employing a $\ell_\infty$ framework, we show how tractable Linear Programming (LP) methods can be used to obtain the worst attack design. Moreover, we provide a controller synthesis iterative method to minimize the worst impact of such attacks.