Optimal Multiple Controlling Nodes Problem for Multi-agent Systems via Alt-PageRank*

In this paper, we deal with problems of finding optimal input nodes of multi-agent systems in the sense of convergence rates of the all agents’ states to an identical value. We consider two cases; Weakly Controlled Systems and Directly Controlled Systems, respectively, and show that in the both cases, the optimal nodes can be given by using an alternative index of PageRank, called Alt-PageRank, which we originally proposed in Yamamoto and Tsumura (2011). In particular, we clarify that Alt-PageRank is also an effective index in multiple input nodes case.