Optimizing Pinned Nodes to Maximize the Convergence Rate of Multiagent Systems with Digraph Topologies

Algorithm 1

Searching for the pinned node set that maximizes .

Input:

the Laplacian matrix , the pinning strength , the number of pinned nodes

Output: the pinned node set ;

1: permute the indices of the nodes of graph to transform into the form (19)

2: compute the left eigenvectors of corresponding to and normalize

them with -norm

3: permute the indices of the nodes in the subgraphs to get ,

4: initialize and , with

5: while    do

6: find the smallest and add the node to the node set

:

7: update

8: end while

9: return  ,