Distributed Data-Driven Nash Equilibrium Seeking in Linear Multi-Agent Systems with External Disturbances

This paper investigates distributed Nash equilibrium (NE) seeking in linear multi-agent network games, where agents with unknown dynamics interact over weakly connected directed graphs under external disturbances. By reformulating the NE seeking problem as a cooperative output regulation problem, we develop a data-driven control framework that embeds the internal model principle to achieve disturbance rejection and eliminate steady-state errors. Closed-loop stability and convergence to the unique NE are proven under standard assumptions on stabilizability, detectability, and data richness. Numerical experiments with a mobile robot network demonstrate the method's effectiveness in achieving output NE seeking under noisy measurements and external disturbances.