Transmission Control in Complex Networks Using Modal Methods
Abstract
In this project we develop novel theoretical foundations and algorithmic tools for controlling the flow of signal across a network modeled as a graph. Such signals can be information in context of a communication/social network, amplitude of current/voltage in context of a power grid, or infectious disease in context of network of communities. Signal can spread or be transmitted from a vertex to neighboring vertices across the edges of the graph. The proposed work is organized into three main technical thrusts. In the first thrust of the proposal we address the problem of controlling the multi-scale clustering structure of a network through direct control of vertex states, and achieve that in a distributed, decentralized manner over the network (with each vertex computing its own control command only through neighborhood communication) in order to affect a signal transmission dynamics over the network. In the second thrust we develop novel methods for making a network robust to resonance attacks, in which an adversarial agent periodically pumps signal into the network at a resonant frequency in an attempt to saturate the network with signal. Finally, we develop novel theoretical foundations and algorithms to reason about and control higher-order topological features, such as cycles and holes, in a network using an algebraic approach in order to affect and control signal transmission dynamics over the network. To those ends we develop novel theoretical and algorithmic tools that are fundamentally based on the spectrum of the Laplacian matrices (graph Laplacian as well as higher-order Laplacian) as well as its eigenvectors (the modes of the graph). The proposed technologies not only build the foundations to a better understanding of how signals and information originate, flow and transform within complex networks, but also give novel tools for effectively controlling the flow of such signal, enhancing security and privacy within such networks.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 29, 2024
- Source ID
- FA95502310046
Entities
People
- Subhrajit Bhattacharya
Organizations
- Air Force Office of Scientific Research
- Lehigh University
- United States Air Force