Attack-Resilient Distributed Nash Equilibrium Seeking of Uncertain Multiagent Systems Over Unreliable Communication Networks

This article investigates the distributed Nash equilibrium (NE) seeking problem of uncertain multiagent systems in unreliable communication networks. In this problem, the action of each agent is subject to a class of nonlinear systems with uncertain dynamics, and the communication network among agents will be affected by the nonperiodic denial of service (DoS) attacks. Note that, in this insecure network environment, the existence of DoS attacks will directly destroy the connectivity of the network, which leads to performance degradation or even failure of the most existing distributed NE seeking algorithms. To address this problem, we propose a two-stage distributed NE seeking strategy, including the attack-resilient distributed NE estimator and the neuroadaptive tracking controller. The estimator based on the projection subgradient method and the consensus protocol can converge exponentially to virtual NE against DoS attacks. Then, the neuroadaptive tracking controller is designed for uncertain multiagent systems with the output of the estimator as the reference signal such that the actual action of all agents can reach NE. Based on the Lyapunov stability theory and improved average dwell time automaton, the stability of the estimator and the controller is proven, and all signals in the closed-loop system are uniformly bounded. Numerical examples are presented to verify the effectiveness of the proposed strategy.