Robust Nash equilibrium seeking for multi-agent systems via event-triggered communication and control over directed graphs

This article investigates Nash equilibrium seeking in noncooperative games for multi-agent systems under event-triggered communication and control, with the aim of improving resource efficiency. To reduce communication load and actuator wear caused by continuous communication and actuation, two distributed event-triggered Nash equilibrium seeking strategies are developed. An event-triggered algorithm is first proposed for uncertainty-free multi-agent systems over directed communication graphs, and then extended to systems subject to unknown disturbances and unmodeled nonlinear dynamics by incorporating an extended state observer (ESO) and the robust integral of the sign of the error (RISE) technique. Rigorous Lyapunov-based analysis establishes exponential stability of the Nash equilibrium for ideal systems and asymptotic stability under uncertainties. The designed triggering conditions exclude Zeno behavior. Finally, simulation experiments motivated by practical scenarios validate the proposed algorithms.