Distributed Nash Equilibrium Seeking in Disturbed Multi-agent Systems Under DoS Attacks

This study investigates the problem of achieving distributed Nash equilibrium (DNE) in multi-agent systems (MASs) under denial-of-service (DoS) attacks and external disturbances. Existing approaches often fail to ensure convergence when communication is disrupted and coordination is impaired. To address these challenges, we propose a fully distributed algorithm that combines a linear extended state observer for real-time disturbance estimation with a gradient-based control protocol. Key innovations include: (1) a computationally efficient local behavior estimation strategy based on observed states and gradient information, which replaces global estimation to reduce complexity; and (2) a unified control framework applicable to both first- and second-order MASs, guaranteeing convergence to the DNE despite DoS attacks and external perturbations. Rigorous Lyapunov-based analysis establishes sufficient conditions for stability and convergence. Simulation results demonstrate that the proposed method enables agents to reach the Nash equilibrium under persistent attacks and disturbances, highlighting its robustness and scalability.