Attack-resilient adaptive distributed neurodynamic approach for solving noncooperative games

This paper considers noncooperative games operating under adversarial conditions, including both exploratory and causative attacks, where players' dynamics are subject to private inequality constraints and external disturbances. To address this challenge, we propose an adaptive distributed neurodynamic approach with continuous-time switching communication. Crucially, and in contrast to existing methods that often rely on fixed switching sequences-which can still pose a significant risk of information leakage over time-the communication topology in our framework is designed to switch randomly within a finite set of directed strongly connected graphs. This randomness provides a stronger defense against exploratory attacks like eavesdropping. Under mild conditions on the switching frequency, the convergence of the approach is rigorously proved using singular perturbation techniques, while integrated disturbance-observer-based control ensures effective rejection of external disturbances. To overcome the additional challenges posed by causative attacks and severe communication limitations, this paper further develops an attack-resilient adaptive distributed approach with discrete-time switching communication. This strategy guarantees exponential convergence to the NE even when the communication network is under attack and is rigorously designed to strictly exclude Zeno behavior. Comprehensive simulation results demonstrate that the proposed approaches achieve faster convergence, stronger resilience against both types of attacks, and higher adaptability in dynamic environments compared to existing methods. The practical effectiveness and utility of the approaches are conclusively validated through their application to a self-organizing autonomous vehicle network, confirming their suitability for real-world noncooperative game scenarios.