Resilient Cooperative NE Control for High‐Order Nonlinear MASs Under FDI and DoS Attacks

ABSTRACT This paper studies the resilient cooperative distributed Nash equilibrium (NE) control problem for high‐order nonlinear multi‐agent systems (MASs) subject to hybrid cyber attacks. In contrast to prior research on NE seeking, this work pioneers the study of resilient distributed NE control for nonlinear MASs under denial‐of‐service (DoS) and false data injection (FDI) attacks. To address the challenges posed by this problem, a novel layered NE control framework is introduced, comprising an FDI estimator, a resilient distributed NE seeking strategy, enhanced filters, and an adaptive controller. Specifically, the deep neural networks (DNN)‐based estimator is trained offline to learn the mapping relationship. The resilient distributed NE seeking algorithm is designed to guarantee convergence of the agents' actions to the NE in spite of the presence of hybrid attacks. Subsequently, smooth action signals are generated via dual‐mode hierarchical filtering techniques. By utilizing these refined actions and their derivatives, an adaptive controller is developed to drive the outputs of the MASs toward the NE point. Simulation results are presented to demonstrate the efficacy of the proposed approach.