离散多智能体系统信息一致性的平衡点

Equilibrium of consensus problems for discrete-time multi-agent systems

研究了离散多智能体系统信息一致性的平衡点问题.对于固定通信结构系统,基于非负随机矩阵谱半径及其对应的左特征向量,证明了在系统的通信拓扑所含的生成树中,仅根节点对平衡点有作用.对于时变通信结构系统,根据同阶非负矩阵样式的有限性,证明了在动态通信拓扑的联合中,仅那些到任意节点都存在有向路径的顶点对平衡点有作用.数值算例验证了理论结果的正确性.

The equilibrium of consensus problems for discrete-time multi-agent system is studied.For a fixed topology system,based on the spectrum of nonnegative stochastic matrix and its left eigenvector,it is proved that only the initial conditions of the root vertices contribute to the equilibrium value in interaction topology which contains a spanning tree. For a time-varying topology system,by the fitness of style of nonnegative matrices,it is proved that only the nodes that have directed paths to all the others in the union of switching interaction topology have contributions to the final value. Numerical examples are used to prove the correctness of the theorems.