Sparse false data injection attacks against distributed control of multi-agent systems

• A sparse false data injection attack against multi-agent systems is designed. • The attack signal is decomposed into the bias signal and attack direction vector. • Optimization and linear matrix inequality constitute a two-stage design process. • Both attack effectiveness and stealthiness are considered in the attack design. • Drone simulation and experiment are conducted to illustrate the proposed approach. This paper investigates the design problem of false data injection (FDI) attacks aimed at degrading system performance in multi-agent systems (MASs). We consider a scenario where a limited number of agents can be compromised, which implies that the attack signal exhibits a sparse structure. However, ensuring this sparsity is challenging because of the high dimensionality of the attack signal. To overcome this difficulty, the attack signal is decomposed into two components: the bias signal and the attack direction vector, leading to a two-stage attack strategy design method. In the first stage, we ensure sparsity by exploiting the lower-dimensional structure of the bias signal. To this end, we formulate an optimization problem with an l 0 norm constraint, which is solved using the alternating direction method of multipliers (ADMM). In the second stage, to achieve better attack performance, the attack direction vector is constructed using H − and H ∞ indices in the frequency domain, ensuring both the effectiveness and stealthiness of the attack. Moreover, we derive the ultimate bounds for consensus error and state estimation error induced by the attack. Finally, we provide a hardware-in-the-loop (HIL) simulation in Gazebo platform and a real-world experiment on multiple mobile robots to illustrate the effectiveness of the proposed attack strategy.