Fundamental Stealthiness–Distortion Trade-Offs in Cyber-Physical Systems

In this chapter, we analyze the fundamental stealthiness–distortion trade-offs 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 trade-offs 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.