Analysis and Control of Dynamical Systems on Complex Networks of Unbounded Size
Abstract
Major Goals: Complex networks of dynamical systems arise in many applications such as the Internet of Things (IoT), 5G communications, grid networks, social interactions, epidemic networks and biological neuronal networks, and there is an obvious need to analyze and control such networked systems. The study of the control of systems on complex networks typically involves such notions as controllability, control energy input node selection, the low-complexity control synthesis problems with simplified control (e.g. consensus or synchronization , pinning control, ensemble control, low-rank (e.g. mean field) coupling, and patterned coupling. The first major goal of the project is to place these fundamental notions in a completely new setting when the systems under consideration are distributed over unbounded networks. In a development which was entirely separate from systems and control, the mathematical theory of graphons was created to model large networks and their infinite limits and, furthermore, it was applied to the analysis of purely dynamical models such as the heat equation and coupled oscillator models. This theory has been fully utilized to achieve the objectives the project. The second major gaol of the Principal Investigator and co-workers was to initiate graphon systems and control theory to develop a control theory and methodology of large-scale network-coupled linear dynamical systems, where a particular feature of this theory is that it permits the generation of low-complexity approximate solutions to problems on large networks which would otherwise be intractable. Linear regulator graphon systems and control theory is based upon both the sophisticated theory of graphons and on the well established infinite dimensional linear system theory presented. We observe that this work follows the spirit of mean field game theory and, indeed, in another project a theory of so-called Graphon Mean Field Games was developed and was interlinked with this project.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 14, 2022
- Accession Number
- AD1229593
Entities
People
- Peter E. Caines
Organizations
- McGill University