Optimal topology of multi-agent systems with two leaders: a zero-sum game perspective

• DOI: 10.48550/arxiv.1410.7026
• Publication Date: 2014-01-01
• Authors: Jingying Ma; Yuanshi Zheng; Bin Wu; Long Wang
• Keywords: Topological graph theory; Strongly connected component

It is typical to assume that there no conflict of interest among leaders. Under such assumption, it known that, for a multi-agent system with two leaders, if the followers' interaction subgraph undirected and connected, then followers will converge convex combination leaders' states linear consensus protocol. In this paper, we introduce between leaders: by choosing k connect with, every leader attempts all himself closer than other. By using graph theory matrix theory, formulate as standard two-player zero-sum game give some properties about it. noteworthy here generated from Interestingly, find optimal topology equivalent solve Nash equilibrium. Especially case one connected follower, necessary sufficient condition an be given. Moreover, circulant or center node, system's obtained. Simulation examples are provided validate effectiveness theoretical results.