Submodularity-based False Data Injection Attack Scheme in Multi-agent Dynamical Systems

TL;DR

This paper introduces a submodularity-based approach to design false data injection attacks in multi-agent systems, enabling the attacker to maximize consensus error efficiently with near-optimal algorithms.

Contribution

It formulates the attack design as a submodular optimization problem and develops greedy algorithms with proven bounds for selecting compromised agents.

Findings

The attack problem is NP-hard but can be approximated efficiently.

The proposed greedy algorithms achieve near-optimal attack effectiveness.

Simulations confirm the effectiveness and efficiency of the algorithms.

Abstract

Consensus in multi-agent dynamical systems is prone to be sabotaged by the adversary, which has attracted much attention due to its key role in broad applications. In this paper, we study a new false data injection (FDI) attack design problem, where the adversary with limited capability aims to select a subset of agents and manipulate their local multi-dimensional states to maximize the consensus convergence error. We first formulate the FDI attack design problem as a combinatorial optimization problem and prove it is NP-hard. Then, based on the submodularity optimization theory, we show the convergence error is a submodular function of the set of the compromised agents, which satisfies the property of diminishing marginal returns. In other words, the benefit of adding an extra agent to the compromised set decreases as that set becomes larger. With this property, we exploit the greedy scheme to find the optimal compromised agent set that can produce the maximum convergence error when adding one extra agent to that set each time. Thus, the FDI attack set selection algorithms are developed to obtain the near-optimal subset of the compromised agents. Furthermore, we derive the analytical suboptimality bounds and the worst-case running time under the proposed algorithms. Extensive simulation results are conducted to show the effectiveness of the proposed algorithm.