异质多智能体系统二分一致性的充要条件

针对由一阶智能体和二阶智能体组成的异质多智能体系统的二分一致性问题,对连续和离散系统情形分别设计了二分一致性协议。基于结构平衡的拓扑,通过规范变换实现了从具有敌对关系的系统到具有非负连接权重系统的转化，将二分一致性问题转变为一般一致性问题。进一步,运用代数图论和矩阵理论分析闭环控制系统的动态特性,得到了异质多智能体系统渐近实现二分一致性的充要条件。最后通过数值模拟验证了所得结果的有效性。

Necessary and sufficient conditions for bipartite consensus of heterogeneous multi-agent systems

To investigate the bipartite consensus problem of heterogeneous multi-agent systems composed of first- and second-order agents, in this study, we designed bipartite consensus protocols for continuous and discrete systems. Based on a structurally balanced topology, we employ gauge transformation to transform a system with antagonistic interactions into one with non-negative connection weights. Accordingly, the bipartite consensus problem is transformed into a general consensus problem. We use algebraic graph theory and matrix theory to analyze the dynamic characteristics of the closed-loop control system and obtain the necessary and sufficient conditions to guarantee that heterogeneous multi-agent systems reach bipartite consensus asymptotically. Finally, we present numerical simulations to illustrate the effectiveness of the obtained theoretical results.