Minimum leader selection for Structural Controllability of Undirected Graphs with Leader-follower Framework

TL;DR

This paper introduces a new concept called minimal perfect critical set (MPCS) to find the minimum leader set for controlling undirected graphs, providing exact solutions for specific network types.

Contribution

It proposes MPCS as a novel approach to solve the minimum leader selection problem and fully solves it for deterministic scale-free networks and Cayley trees.

Findings

MPCS helps identify optimal leader sets for controllability.

Complete solutions are provided for DSFN and Cayley trees.

The approach advances understanding of leader selection in network control.

Abstract

The optimization problem of the minimum set of leaders for the controllability of undirected graphs are addressed. It is difficult to find not only its optimal solution but also its approximate algorithm. We propose a new concept, namely minimal perfect critical set (MPCS), to obtain an optimal solution. Some properties are presented, and on the basis of these theorems, the problem of the minimum set of leaders of two typical self-similar bipartite networks, namely deterministic scale-free networks (DSFN) and Cayley trees, is solved completely.