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

In this article, Nash equilibrium seeking in the N-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 N-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 N-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 N-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. Note to Practitioners—This article was motivated by the formation control of multiple ground vehicles but can also be applied to other cooperative and competitive tasks of second-order multi-agent systems. While some existing works designed control laws for specific tasks with limited applicability, this article provides a new game-theoretical method to accomplish a wide range of control tasks for multi-agent systems. By building a game-theoretic model and designing appropriate cost functions, the proposed N-coalition Nash equilibrium seeking strategy can serve as the control law to drive the multi-agent system to desired states. Notably, the proposed algorithm ensures the multi-agent system achieves its objective within a prescribed time under event-triggered communication, thereby reducing the communication load. This article outlines the conditions for convergence and how to apply the proposed algorithm. The simulation experiments verify the feasibility of this algorithm, but it has not yet been tested on a real system. Future research will involve testing on real-world applications and considering unmodeled nonlinearities and switching topologies.