Dynamic Event-Triggered Mechanism for Distributed Nash Equilibrium Seeking Under Switching Topologies

This article studies distributed Nash equilibrium seeking of a group of players based on an event-triggered mechanism under switching interaction topologies. First, a dynamic event-triggered function is proposed, which relies on the gradient of the player's payoff function and the triggering state information of its neighbors. It enables a rapid response to system changes and is able to effectively eliminate the Zeno behavior. Next, to maintain the strong connectivity in the directed graph for the links switched by the event-triggered mechanism at all times, a switching-triggered communication mechanism is designed in which triggered conditions are enhanced to include the instants of each player's link changes. Furthermore, by restricting switching frequency, this article establishes sufficient conditions with parameter ranges for exponential convergence to the Nash equilibrium. Finally, simulation results show the validity of the proposed strategy.