Leader Selection in Complex Networks for Controllability and Energy Efficiency
Abstract
This report investigates the controllability and energy-related controllability of complex networks. Specifically, our objective is to establish controllability characteristics of signed complex networks, where the network units interactwith each other via linear consensus dynamics and the network admits positive and negative edges to capture cooperative and competitive interactions among these units. The network units can be classified into leaders and followers. For network controllability, graphical characterizations of the controllability of signed networks are first developed based on the investigation of the interactions between network topology and unit dynamics. Since signed path and cycle graphs are basic building blocks for a variety of networks, the developed topological characterizations are then exploited to develop leader selection methods for signed path and cycle graphs to ensure the network controllability. Heuristic algorithms are also developed showing how the leader selection methods developed for path and cycle graphs can be potentially extended to more general signed networks. As the control energy metrics, the Gramian-based control energy measures are exploited to quantify the difficulty of the control problem on signed networks in terms of the required control energy and system performance. Fundamental relationships between these measures and the network topology are developed via graph Laplacian to characterize the energy-related controllability. It is revealed that, for the structurally unbalanced signed graphs, the energy-related controllability is closely related to the diagonal entries of the inverse of the graph Laplacian. It is also discovered that the structurally balanced signed graphs and their corresponding unsigned graphs have the same energy-related controllability.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 06, 2020
- Accession Number
- AD1111194
Entities
People
- Shaoping Xiao
Organizations
- University of Iowa