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This article considers Nash equilibrium (NE) seeking of networked mean field games (NMFGs) with event-triggered strategies in a fully distributed manner. To simplify the formulation of distributed online decision-making problems over a network, we introduce the NMFG over a spatiotemporal domain for large-scale equilibrium computation. By merging ideas from estimation theory and consensus theory, three parallel auxiliary variables are designed to dynamically estimate the aggregative behavior of the collection, called the mean field term. The leaderless consensus of players’ estimates and the optimization of local objective function need to be achieved simultaneously. In addition, the dynamic event-triggered mechanism and adaptive learning gain are introduced, which provide a natural and scalable framework for distributed communication and computation in large-scale complex networks. We further prove that convergence to NE can be guaranteed using the designed strategies. Finally, a numerical experiment is provided to validate the proposed algorithm.

This article investigates for the first time the predefined-time relative position tracking and attitude synchronization control problem with asymptotic tracking errors for spacecraft. Compared to previous studies, this article considers convergence speed and control accuracy simultaneously, ensuring the predefined-time stability and asymptotic convergence of the spacecraft relative tracking errors. The fuzzy logic systems are introduced to estimate the unknown nonlinear terms in the relative dynamic model. By combining the adaptive backstepping control method and the command filter technique, a relative position tracking and attitude synchronization control method is proposed. The improved filter compensation signals are designed to eliminate the impact of filtering errors on the control performance. With the proposed control method, the closed-loop spacecraft position and attitude control system can achieve predefined-time stability, and the spacecraft relative tracking errors can reach zero as time approaches infinity. Finally, simulation results are provided, fully demonstrating the effectiveness of the proposed method.