Prescribed-Time Event-Triggered <i>N</i> -Coalition Nash Equilibrium Seeking for Disturbed Second-Order Players and Its Application

In this article, Nash equilibrium seeking in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i>-coalition noncooperative game is studied for the second-order disturbed players. In this formulation, players are divided into different coalitions. Each coalition acts as a virtual player in the noncooperative game, but the real decision-maker is the individual player. Players within the same coalition work together to minimize the cost function of the coalition they belong to, while each coalition competitively minimizes its own cost function. A prescribed-time event-triggered <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i>-coalition Nash equilibrium seeking strategy is proposed based on the gradient descent method and the dynamic average consensus protocol. The proposed algorithm ensures that the players’ actions converge to the Nash equilibrium of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i>-coalition game within a prescribed time, which can be assigned in advance, without any knowledge of the initial states and the system parameters. Additionally, information exchanges between players only happen when the designed event-triggering condition is met, thereby reducing the communication burden. The prescribed-time stability of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i>-coalition Nash equilibrium is rigorously proven by Lyapunov stability analysis. The Zeno behavior is shown to be prevented until the Nash equilibrium is reached. Finally, the simulation experiments on maneuvering automated ground vehicles demonstrate the effectiveness of the proposed algorithm.