Asymmetric Vulnerability of Measurement and Control Channels in Closed-Loop Systems

This article studies the vulnerability of measurement and control channels in closed-loop systems. The problem of optimal stealthy attacks on linear quadratic Gaussian (LQG) control is analyzed. Different types of stealthiness are considered, including the probability distribution of innovations and their whiteness. For stealthy attacks on two different channels, the worst-case attacks that maximize LQG costs while satisfying different stealthiness constraints are obtained and compared. It is shown that worst-case attacks on the two channels have different properties, which depend on system parameters as well as the threshold of the relaxed stealthiness constraint. The asymmetric vulnerability of the two channels is illustrated by numerical examples.