Centrality-Based Security Allocation in Networked Control Systems

Abstract

This paper addresses the security allocation problem within networked control systems, which consist of multiple interconnected control systems under the influence of two opposing agents: a defender and a malicious adversary. The adversary aims to maximize the worst-case attack impact on system performance while remaining undetected by launching stealthy data injection attacks on one or several interconnected control systems. Conversely, the defender's objective is to allocate security resources to detect and mitigate these worst-case attacks. A novel centrality-based approach is proposed to guide the allocation of security resources to the most connected or influential subsystems within the network. The methodology involves comparing the worst-case attack impact for both the optimal and centrality-based security allocation solutions. The results demonstrate that the centrality measure approach enables significantly faster allocation of security resources with acceptable levels of performance loss compared to the optimal solution, making it suitable for large-scale networks. The proposed method is validated through numerical examples using Erdos-Renyi graphs.

Figures (6)

• Figure 1: Relative gap of the worst-case attack impact between the optimal value and the value given by choosing monitor vertices based on centrality measures. The network size $N = \{ 10, \, 12, \, 14 \}$, the attack budget $n_a = \{1,\,2\}$, and the monitor budget $n_s = 1$. For each network size, $30$ Erdős–Rényi random graphs where an edge is included to connect two vertices with a probability of 0.5.
• Figure 2: Relative gap of the worst-case attack impact between the optimal value and the value given by choosing monitor vertices based on centrality measures. The network size $N = \{ 16, \, 18, \, 20 \}$, the attack budget $n_a = \{1,\,2\}$, and the monitor budget $n_s = 1$. For each network size, $30$ Erdős–Rényi random graphs where an edge is included to connect two vertices with a probability of 0.5.
• Figure 3: Relative gap of the solving time between the optimal value and the value given by choosing monitor vertices based on centrality measures. The network size $N = \{ 10, \, 12, \, 14 \}$, the attack budget $n_a = \{1,\,2\}$, and the monitor budget $n_s = 1$. For each network size, $30$ Erdős–Rényi random graphs where an edge is included to connect two vertices with a probability of 0.5.
• Figure 4: Relative gap of the solving time between the optimal value and the value given by choosing monitor vertices based on centrality measures. The network size $N = \{ 16, \, 18, \, 20 \}$, the attack budget $n_a = \{1,\,2\}$, and the monitor budget $n_s = 1$. For each network size, $30$ Erdős–Rényi random graphs where an edge is included to connect two vertices with a probability of 0.5.
• Figure 5: IEEE 14-bus system.

Theorems & Definitions (6)

• Remark 1
• Theorem 1
• proof
• Theorem 2
• proof
• Definition 1: Centrality measures Golbeck2013Chapter3