Fundamental Stealthiness-Distortion Tradeoffs in Dynamical (Control) Systems under Injection Attacks: A Power Spectral Analysis

In this paper, we analyze the fundamental stealthiness-distortion tradeoffs of linear Gaussian open-loop dynamical systems and (closed-loop) feedback control systems under data injection attacks using a power spectral analysis, whereas the Kullback-Leibler (KL) divergence is employed as the stealthiness measure. Particularly, we obtain explicit formulas in terms of power spectra that characterize analytically the stealthiness-distortion tradeoffs as well as the properties of the worst-case attacks. Furthermore, it is seen in general that the attacker only needs to know the input-output behaviors of the systems in order to carry out the worst-case attacks.