Observer-based FDIAs compensation and event-triggered consensus analysis for nonlinear multi-agent systems

This paper examines the tracking consensus problem in nonlinear multi-agent systems (NMASs) under stochastic false data injection attacks (FDIAs) by integrating an event-triggered framework with a covariance-based observer and an attack compensation scheme. Firstly, to overcome the limitation that each agent can only utilize information from its neighboring nodes, a state observer is constructed by incorporating the minimal upper bound associated with the maximum eigenvalue of the estimation error covariance matrix. Secondly, to suppress the influence of FDIAs on the system, an attack compensator based on the covariance-weighted observer is constructed. Through a combined analysis of the observer and the compensator, it is shown that the state estimation error remains uniformly ultimately bounded, and the minimal upper bound of the maximum eigenvalue of the covariance matrix is derived. Based on this upper bound, a dynamic-threshold event-triggered strategy is developed to improve communication efficiency. Accordingly, a distributed control protocol is formulated to guarantee the tracking consensus of NMASs even under stochastic attacks. Finally, the effectiveness and robustness of the proposed approach are demonstrated through two numerical examples.