Separability of State Trajectories and its Applications to Security of Cyber-Physical Systems

Abstract

This article studies a fundamental problem of security of cyber-physical systems (CPSs). We focus on a class of attacks where some of the actuators could be malicious while all the sensors are considered to be honest. We introduce a novel idea of separability of state trajectories that are generated by the honest and corrupt actuators, and establish its connection to the security of CPSs in the context of detecting the presence of malicious actuators (if any,) in the system. As a defense strategy to guard the CPS against malicious attacks, we focus on the mechanism of perturbing the pre-determined control action by injecting a certain class of random process by the honest actuators called private excitation, which is assumed to have a known distribution. As primary contributions we give sufficient conditions for the existence and non-existence of a separator for linear time-invariant stochastic systems, under the assumption that the policies are randomized-Markovian and randomized history dependent. Several technical aspects of the established results are discussed extensively.Comment: 26 page