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

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.