  Systematic attack design is essential to understanding the vulnerabilities of
cyber-physical systems (CPSs), to better design for resiliency. In particular,
false data injection attacks (FDIAs) are well-known and have been shown to be
capable of bypassing bad data detection (BDD) while causing targeted biases in
resulting state estimates. However, their effectiveness against moving horizon
estimators (MHE) is not well understood. In fact, this paper shows that
conventional FDIAs are generally ineffective against MHE. One of the main
reasons is that the moving window renders the static FDIA recursively
infeasible. This paper proposes a new attack methodology, moving-horizon FDIA
(MH-FDIA), by considering both the performance of historical attacks and the
current system's status. Theoretical guarantees for successful attack
generation and recursive feasibility are given. Numerical simulations on the
IEEE-14 bus system further validate the theoretical claims and show that the
proposed MH-FDIA outperforms state-of-the-art counterparts in both stealthiness
and effectiveness. In addition, \textcolor{blue}{an experiment on} a
path-tracking control system of an autonomous vehicle shows the feasibility of
the MH-FDIA in real-world nonlinear systems.
