Fully Distributed Adaptive Fuzzy Resilient Nash Equilibrium Seeking for Uncertain Multiagent Systems With Prescribed-Time Convergence

Abstract

This article focuses on the prescribed-time fully distributed Nash equilibrium seeking (PT-FDNES) against denial-of-service attacks of multiagent systems (MASs), where the action of each agent is described by high-order uncertain nonlinear dynamics. Specifically, the fuzzy logic system technique is utilized to approximate the unknown nonlinear functions existing in the agents' dynamics, where a single parameter updating law is proposed by estimating the norm of fuzzy optimal weight vectors to further reduce the computational cost. To deal with the difficulty where the attack-induced topologies may destabilize the NE seeking performance, a novel PT function together with a resetting mechanism is delicately designed. Then, a PT-FDNES with adaptive gains is developed by incorporating the resetting mechanism to search for the NE independent of any global information. Subsequently, a novel PT fuzzy adaptive tracking control law is designed in the celebrated backstepping structure. Based on the Lyapunov stability theory, we prove that actions of the MAS converge to the NE within the PT and all the closed-loop system signals remain bounded. At last, an example is given to illustrate the effectiveness of the proposed algorithm.