CAREER: Graphs, geometry and algorithms for sparse decentralized control systems

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

Objective: In recent years, a new paradigm for control systems, now increasingly seen as a collection of interacting autonomous agents, has emerged. A decentralized power distribution system, a formation of unmanned autonomous vehicles used for aid or even package delivery, terrestrial vehicles platoons, and auctions systems are all control systems built around this new paradigm. Similarly, progress in the biological sciences and the need to provide comprehensive and affordable healthcare have made the mapping of complex genetic, metabolic and more recently disease networks commonplace. Intellectual merit: The research deals with a novel framework that unites ideas from graph theory, computer science and dynamical systems. The focus is on control-theoretic methods that are broad enough to address the relevant questions arising in various application settings, yet specific enough to yield implementable methods and algorithms. Specific questions include: how to characterize the minimal communication structure needed to accomplish a task (which links are necessary for the ensemble to cooperate, and which ones are redundant?), how to quantify the resistance of a network to attacks and link failures (what is a good measure of robustness?), how to construct networks accomplishing a given task (what is the most economical network design?). Broader Impacts: The work proposed here will provide key technologies to enable the deployment and analysis of large-scale, secure and efficient multi-agent systems. Over the course of the past twenty years, the paradigm of centralized control systems has faded in favor of systems that are large-scale, heterogeneous, sometimes ad-hoc, and decentralized. Because the proposed framework directly relates the dynamics to the underlying network, its potential applications span the various subfields where networked dynamics appear, including, but not limited to, distributed optimization, the study of metabolic networks, formation control, and decentralized power distribution.