Large scale, pervasive communication systems are an important part of everyday life and, with the emergence of the Internet of Everything technology, are becoming an essential part of our infrastructure. Future communication systems necessitate significantly new design paradigms because they are large scale and involve a complex interaction of communications, "natural" (environmental) networks as well as control. The seamless management of a system of this complexity, interconnection, and scale is daunting. A fundamentally new approach is needed to tackle the issues of scale and complexity. The investigators are studying novel mathematical models for network design and optimization for systems of much larger size than those that are tractable with current methods. They are planning to demonstrate their utility on applications such as cognitive radio, wireless body area sensing networks and potentially models for bacterial populations. The new methods have the potential to impact the design and control of very general, large-scale networks such as biological, social networks and the SmartGrid.
This research develops a novel theoretical framework to address the challenges of large scale system design by analyzing, tracking, and controlling Markov processes over graphs associated with complex systems. The correlation induced in these large Markov chains is exploited via sparse approximation theory employing graph wavelets for representation. Typical complex systems induce an underlying sparsity that enables dimensionality reduction via compressed sensing-like schemes. This research develops new sparse techniques for formal modeling, analysis and optimization of large-scale systems that evolve temporally, by designing novel graph wavelets for directed graphs, in combination with new sparse approximation algorithms and control methods tailored to the complex systems for estimation, communication and control.
