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

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 maximize the consensus convergence error by compromising a subset of agents and manipulating their local high-dimensional states. We first formulate the FDI attack design problem as a combinatorial optimization problem, which is NP-hard. Then, based on the submodularity optimization theory, we provide the necessary and sufficient conditions to guarantee the submodularity of the objective function, which satisfies the property of diminishing marginal returns. In other words, the profit of adding an extra agent to the compromised set decreases as that set becomes larger. With this property, we exploit the greedy scheme which aims to find the optimal compromised agent set to produce the maximum convergence error when adding one extra agent to that set each time. Thus, an FDI attack selection algorithm is formed 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 algorithm. Extensive simulation results are conducted to show the effectiveness of the proposed algorithm.