Gramian‐based vulnerability analysis of dynamic networks

Abstract

Abstract In this paper, the vulnerability of large‐dimensional dynamic networks to false data injections is analysed. The malicious data can manipulate input injection at the control nodes and affect the outputs of the network. The objective is to analyse and quantify the potential vulnerability of the dynamics by such adversarial inputs when the opponents try to avoid being detected as much as possible. A joint set of most effective actuation nodes and most vulnerable target nodes are introduced with minimal detectability by the monitoring system. Detection of this joint set of actuation‐target nodes is carried out by introducing a Gramian‐based measure and reformulating the vulnerability problem as a standard optimisation problem. However, the underlying optimisation problem appears to be a binary program and intractable in large‐dimensional systems. Balanced realisation of the system dynamics, combined with a Gauss–Newton approach is employed to provide a two‐stage algorithm for the selection of the most effective joint sets. The proposed approach relies on QR decomposition and QR pivoting, does not require iterative computation of Gramian matrices, and scales well with the system dimensions. The proposed approach is evaluated on a set of synthetic and real‐life examples including IEEE 118 bus power network.