Systems Theory for Large Scale Systems

Academic advisor: Ulf Jönsson

Sponsor: Swedish Research Council (VR)

The goal of this project is to develop theory and algorithmic tools for rigorous design and analysis of large-scale networks of dynamical systems. The project is motivated by applications that continuously evolve by the addition or removal of components and where the sheer size of the system makes exact analysis and design computationally intractable. Examples of application areas showing these characteristics are communication networks such as the Internet, wireless communication networks, the power grid, and some problems in systems biology multi-vehicle systems.

The project offers a wide range of possible research directions with varying theoretical contents and application domain. Three possible directions are

• Control and complexity of heterogeneous networks: Networked control applications pose challenging problems that shift the focus of the research from individual feedback loops to systems with complex interconnection topology and the design of decentralized control algorithms. A major obstacle is that most traditional control theoretic algorithms scale poorly with the system dimension and become intractable when applied to networked systems. In this project we consider model simplifications that explore structure in order to reduce the complexity of analysis and design.
• Switching networks: In this project we consider decentralized control problems where feedback performance can be improved using switching or time-periodic compensation. One example application is in coordination of multi-agent systems using, where improved convergence rates can be obtained if information is exchanged over a time-switched network rather than a static communication network.
• Communication networks: This project focuses on distributed control algorithms in wireless communication and Internet congestion control. The problem is to obtain fair and efficient resource allocation in the network using only local information as basis for the feedback.