H Infinity Minimal Destabilizing Feedback for Vulnerability Analysis and Attack Design of Nonlinear Systems

TL;DR

This paper explores how minimal feedback attacks can destabilize nonlinear systems by leveraging robust control theories, revealing vulnerabilities even when linear approximations suggest stability.

Contribution

It introduces a novel analysis of minimal destabilizing feedback attacks on nonlinear systems, extending linear perturbation results to the nonlinear context.

Findings

Minimal destabilizing attacks can push nonlinear systems to instability boundary.

Linear destabilization does not necessarily imply nonlinear destabilization.

Increasing attack gain guarantees internal destabilization for broad nonlinear system classes.

Abstract

The robust stability problem involves designing a controlled system which remains stable in the presence of modeling uncertainty. In this context, results known as small gain theorems are used to quantify the maximum amount of uncertainty for which stability is guaranteed. These notions inform the design of numerous control systems, including critical infrastructure components such as power grids, gas pipelines, and water systems. However, these same concepts can be used by an adversary to design a malicious feedback attack, of minimal size, to drive the closed-loop system to instability. In this paper, we first present a detailed review of the results in robust control which allow for the construction of minimal destabilizers. These minimally sized attacks merely push the system to the stability boundary, which we demonstrate do not necessarily destabilize nonlinear systems even when the linearization is destabilized. Our main result leverages linear perturbation theory to explicitly prove, in the state space context, that internal destabilization is guaranteed for a broad class of nonlinear systems when the gain of these attacks is slightly increased.