Operator Methods for Analysis and Control of Dynamics, Networks, and Dynamic Networks
Abstract
The explosion of data-driven applications in recent years has led to the creation of an arsenal of effective tools for the analysis of complex networks, for tasks such as clustering, community detection, visualization, ranking, and more. At the same time, new data-driven methods in dynamical systems have enabled one to identify invariant sets, coherent sets, and other features directly from data. These two seemingly distinct areas are actually closely related: when viewed from a certain perspective, dynamical systems may be viewed as networks, and vice versa. The goal of this project is to develop a suite of techniques for data-driven analysis of complex systems, including networks, dynamical systems, and networks that are changing in time (dynamic networks"). The common thread that runs throughout this proposed work is the spectral analysis of linear operators that describe either the underlying dynamics, or the underlying network structure. For dynamical systems, the relevant operators are the Koopman and Perron-Frobenius operators; for networks, they are the adjacency matrix, graph Laplacian, and variants of these.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Oct 31, 2018
- Source ID
- W911NF1710512
Entities
People
- Clarence W. Rowley
Organizations
- Army Contracting Command
- Princeton University
- United States Army