Adaptive Nash Equilibrium Seeking in Hybrid Heterogeneous Open Multi-Agent Systems Under DoS Attacks

This paper investigates the problem of adaptive Nash equilibrium (NE) seeking in hybrid heterogeneous open multi-agent systems (MASs) under Denial-of-Service (DoS) attacks. In the considered open MASs, agents can join or leave the network at any time, which leads to a changeable system size. To address this challenge, we propose a fully distributed control framework that enables agents with heterogeneous dynamics to converge to NE at an exponential rate, using only limited information exchange and localized computation. Additionally, an adaptive strategy is introduced, where the control gains of each agent are adjusted based on local adjacent information. This adjustment allows the system to adapt in real-time to environmental changes. We establish sufficient conditions for the existence of NE in both fixed and varying agent numbers, even in the presence of DoS attacks. Through rigorous theoretical analysis, the proposed adaptive algorithm is proven to guarantee the convergence of the hybrid heterogeneous MAS to the NE despite sustained or intermittent DoS attacks. Numerical simulations are provided to demonstrate the effectiveness of the proposed framework for open MASs in adversarial environments.