Game-Based Consensus of Hybrid Multiagent Systems

This article considers consensus of first-order/second-order hybrid multiagent systems (MASs) based on game modeling. In the first-order hybrid MAS (HMAS), a subset of agents select the Nash equilibrium of a multiplayer game as their states at each game time and the others update their states with first-order continuous-time (C-T) dynamics. By graph theory and matrix theory, we establish sufficient and necessary conditions for consensus of the first-order HMAS with two proposed protocols. The second-order HMAS is composed of agents whose states are determined by the Nash equilibrium of a multiplayer game and agents whose states are governed by second-order C-T dynamics. Similarly, sufficient and necessary conditions are given for consensus of the second-order HMAS with two proposed protocols. Several numerical simulations are provided to verify the effectiveness of our theoretical results.