Vulnerability analysis for a class of nonlinear cyber–physical systems under stealthy attacks

Abstract

This article studies the vulnerability for a class of nonlinear cyber–physical systems under stealthy attacks, i.e., whether the attack is able to destabilize the system and not be detected by the attack detector. Both non-stochastic and stochastic attacks are considered. The residual’s norm is used to characterize the stealthiness of non-stochastic attacks. The nonlinear system is decomposed into two decoupled subsystems. By analyzing the boundedness of subsystems’ states under stealthy attacks, a sufficient condition for vulnerability is given. Furthermore, a stochastic attack is designed to destabilize the system with the Kullback–Leibler divergence (KLD) adopted to describe the stealthiness. To ensure stealthiness, the attack’s parameters are carefully chosen such that the upper bound of the KLD is no larger than the threshold. A sufficient condition for the existence of such attack is given. Finally, a numerical example of the fixed-base inverted pendulum is illustrated to verify the theoretical results.