Multiagent system controllability evaluation using the multilevel structure of the graph of agents

A new approach is proposed to the calculation of the upper and lower bounds of the multiagent system controllability index formalized as the existence probability of the path from any node to the control center with the message transmission time not larger than the constant t. Controllability is one of the properties of this system that determines the stability of its functioning. A regular graph in the form of a tree with virtual nodes, which makes it possible to apply the methods of calculating the number of vertices in a particular level, is proposed in order to compute controllability boundaries.