Optimal Design of Stealthy Attacks in Partially Observed Linear Systems: A Likelihood-Based Approach

TL;DR

This paper develops a likelihood-based detection method and an optimal control framework for designing stealthy attacks on partially observed linear systems, balancing attack success and detectability.

Contribution

It introduces a novel likelihood-based detection mechanism and a hierarchical control approach for optimal stealthy attack design under different information structures.

Findings

The proposed detection mechanism effectively quantifies stealthiness.

The hierarchical optimization yields semi-explicit solutions for adaptive attacks.

Numerical experiments demonstrate the impact of information constraints on attack stealthiness.

Abstract

We study the optimal design of stealthy attacks against partially observed linear control systems. We first propose a novel likelihood-based detection mechanism derived from the innovation process, based on which we quantify stealthiness and formulate an attack design problem that trades off performance degradation and detectability. We develop a tractable control-theoretic framework for optimal stealthy attacks under two information structures: deterministic attacks fixed prior to system evolution, and adaptive attacks constructed from available observations. In the adaptive setting, the attacker's partial observation leads to a stochastic control problem with an endogenous information structure. We address this challenge through a hierarchical optimization framework combined with the separation principle, reducing the problem to a Markovian control formulation and yielding semi-explicit optimal attacks. We further establish well-posedness of the resulting systems and illustrate through numerical experiments how information constraints shape the trade-off between attack effectiveness and stealthiness.