Predefined-time convergence strategies for multi-cluster games in hybrid heterogeneous systems

This paper explores the problem of (generalized) Nash equilibrium search in multi-cluster games with heterogeneous dynamics and multiple constraints. Within this research framework, each agent acquires information solely through local interactions with its neighbors and forms clusters based on similarity of interests. These clusters manifest dual relationships of cooperation and competition: agents within the same cluster enhance decision-making capabilities through cooperation, while different clusters compete to maximize their respective benefits. To delve into these complex interactions among clusters and the learning and evolution processes among agents, four distributed control algorithms suitable for various scenario requirements are designed and implemented. These algorithms ensure that each agent converges to a Nash equilibrium (NE) or generalized Nash equilibrium (GNE) of the multi-cluster system within predefined time points. Finally, we apply these algorithms to the connectivity control problem of unmanned aerial vehicle swarms with diverse dynamics, validating the theoretical results through comprehensive simulations.