Distribution-Free Budgeted Stealthy Attack Scheduling for Remote State Estimation

Abstract

This letter addresses budgeted stealthy false-data-injection (FDI) scheduling against remote state estimation, where a resource-constrained adversary may corrupt at most a fraction $\barΓ$ of transmissions. Existing event-triggered schedulers invert a Gaussian innovation tail to set the firing threshold and certify stealth by covariance matching; both are exact only under Gaussianity, which real cyber-physical residuals routinely violate. We propose a distribution-free scheduler pairing the worst-case FDI action with a split-conformal calibrated trigger, requiring neither the plant matrices nor any distributional model. We establish exact pathwise stealth against every magnitude-measurable detector, for any firing rule and innovation law; a finite-sample distribution-free bound on the mean firing rate, with almost-sure budget attainment under stationarity and ergodicity; and a steady-state degradation identity linear in a single scalar energy capture $ψ$, maximized by the same order statistic that delivers the budget guarantee. A conditional sign-symmetry condition delimits when the certificate extends to sign-sensitive detectors, the residual exposure being governed by a fourth cumulant that vanishes under Gaussian noise. Monte-Carlo studies and a heavy-duty truck CAN record confirm the bounds and quantify what the Gaussian assumption costs outside its regime.