Katz Centrality-Based Security Allocation in Positive Networks
This paper deals with security allocation challenges for networked control systems represented by positive-weighted digraphs under stealthy false data injection attacks. These systems consist of interconnected subsystems, referred to as nodes in the underlying digraph, where an adversary aims to maximize network performance loss by stealthily attacking specific nodes. Meanwhile, a defender monitors several nodes to impose stealthiness constraints on the adversary's actions, thereby minimizing the network performance loss. We analyze the worst-case network performance loss of these stealthy attacks and make the following contributions: we (i) show that the worst-case network performance loss is upper-bounded by a tractable semi-definite programming (SDP) problem; (ii) establish the relationship between the SDP problem and the Katz centrality measure of the underlying digraph under a sufficient condition, resulting in a network-size-independent optimization problem; and (iii) provide a heuristic search based on the Katz centrality measure of the underlying digraph for selecting sub-optimal monitor nodes against all admissible attack scenarios without solving optimization problems. These results offer practical insights for safeguarding large-scale networked control systems against stealthy false data injection attacks. The obtained results are validated via extensive simulations on Erdos-Renyi random graphs with different network sizes.