Game-Based Consensus of Switching Multi-Agent Systems

This paper investigates the leader–follower consensus problem for a class of second-order multi-agent systems. These systems are composed of both discrete-time and continuous-time subsystems and are governed by switching dynamics. Within the framework of a fixed directed topology involving multiple leaders, two control strategies are formulated. One applies separate control protocols to the continuous and discrete subsystems, while the other adopts an unified sampled-data control protocol. First, a multi-player game model is established based on the analysis and simulation of conflict behaviors among agents, and the existence of a unique Nash equilibrium(NE) for the system is proven. Then, based on the Nash equilibrium, a continuous–discrete-time game-based switching control system is formulated. Furthermore, the results confirm that the proposed system achieves consensus under both control strategies, even under arbitrary switching patterns. Finally, the performance of the approach is verified through numerical simulations.