Nash Equilibrium Seeking for Hybrid Heterogeneous Euler–Lagrange Systems in Multicluster Games Under DoS Attacks: A Predefined-Time Approach

Abstract

This article investigates the problem of generalized Nash equilibrium (NE) seeking in multicluster games involving hybrid heterogeneous Euler–Lagrange (EL) systems under denial-of-service (DoS) attack. Each cluster aims to minimize its payoff function, integrating noncooperative games with distributed optimization in a unified framework. Traditional generalized Nash equilibrium (GNE) seeking methods often assume linear dynamics, which are insufficient for real-world applications involving nonlinear hybrid heterogeneous EL systems. Initially, the problem is addressed without considering DoS attacks, where a distributed predefined-time control method is developed to achieve GNE among players in the multicluster game. This approach ensures convergence to the NE within a predefined-time frame. Moreover, in complex DoS environments, achieving GNE becomes challenging when the communication links between agents are attacked. To address this, we propose a topology reconstruction method by restoring and reconnecting the communication connection based on their positions. Meanwhile, the sufficient conditions to GNE seeking in predefined-time under DoS attacks are presented. Numerical simulations are provided to validate the effectiveness of our method in multicluster game scenarios, demonstrating its practical applicability in both DoS attacks and non-attack situations.