False Data-Injection Attack Detection in Cyber-Physical Systems: A Wasserstein Distributionally Robust Reachability Optimization Approach

The paper’s Lemma 2 correctly gives an exact LMI reformulation (22) for the FAR DRCC via Wasserstein duality, and Theorem 2 claims an exact finite reformulation (23) of (21). However, in (23) the block for the confidence-set DRCC omits the necessary hinge epigraph that links the per-sample variables to the dual scalar γ (the variable vi even appears in the minimization list but is unused). As written, (23) lacks constraints like vi ≥ γ − ui and vi ≥ 0, which are required by the standard dual characterization; without them, the Q-analog is not equivalent to (21c) . This omission is implicitly corrected later in the algorithmic subproblem (26), where the missing relations are included (modulo a small notational typo η→γ), restoring the exactness of the reformulation . The model solution supplies precisely these missing pieces, deriving (22) and the Q-analog from the exact Wasserstein dual for indicator losses and an exact SDP for distances to quadratic superlevel sets, and it retains the reachability LMI (19), thereby establishing the intended equivalence between (21) and (23) .