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From Cycle Space to Cycle Manifold: Limits and Achievability of Blind False Data Injection Attacks

arXiv · AI, language, vision and robotics · article · Sep 9, 2026 · UTC

A false data injection attack (FDIA) can change the estimated grid state while evading a residual-based bad data detector (BDD). Existing blind attacks learn a low-rank measurement subspace, but this algebraic view does not state the physical grid constraints that make an attack stealthy or the minimum information needed to recover the complete attack space. Under the connected direct-current (DC) branch-flow model, we show that the residual-sensitive subspace of the noiseless orthogonal test is exactly the weighted cycle space. Its orthogonal complement is therefore the complete stealthy atta

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