Fully distributed fuzzy adaptive control for nonlinear multi-agent systems with undirected/directed networks against FDI attacks

• A novel fuzzy observer is proposed to defend against FDI attacks with superior robustness. • An error compensation mechanism reduces reliance on high-precision fuzzy systems and lowers computational load. • A fully distributed protocol is proposed, requiring no global information for scalability and robustness. • The framework unifies security control and error compensation under challenging directed networks for the first time. This paper investigates the fully distributed fuzzy adaptive tracking control problem for nonlinear multi-agent systems (MASs) subjected to dual-channel false data injection (FDI) attacks, and both undirected and directed communication cases are considered. The challenge of the research lies in that the system states, nonlinear terms, and cyber attack signals are all unknown, and only corrupted measurement outputs are available. To solve this problem, firstly, a fuzzy adaptive multivariate observer is designed to estimate all the unknown factors. The proposed method demonstrates better robustness than existing results and enables real-time observation of more general attack signals. Secondly, a novel error-compensation-based fully distributed tracking controller is constructed, which can effectively relax the high demand for fuzzy approximation accuracy in traditional fuzzy adaptive control methods. Thirdly, the results are generalized to a directed communication scenario, which for the first time achieves the combination of the error compensation mechanism, security control mechanism, and fully distributed mechanism in MASs under a directed communication topology. Finally, an application simulation and a comparative simulation are provided to demonstrate the effectiveness and advantages of the proposed methods.