Building Delay-Tolerant Graphs for Coupled LTI Systems

Abstract

Coupled network systems arise all around us, i.e. neural networks, traffic flow, gene regulation networks, synthetic biology, social networks, energy supply chains, coordination of autonomous vehicles. All these systems however suffer from inter-agent interaction latencies, also known as time delay. Delay is known to cause catastrophic effects in networks; it affects decision making, response time, which may then negatively influence the dynamics of spreading virus, signal transmission in neurons, human reaction times in car driving, when controlling multiple unmanned aerial vehicles, and when maneuvering the Mars Rovers. Although the detrimental effects of delays in networks have been recognized, this was overlooked in the analysis and synthesis of networks and associated graphs.

In this poster presentation, we present our recent work on bridging two core concepts on a benchmark linear time invariant (LTI) system: network structure (related to graph) and time delay. Specifically, we study the relationship between graph structure, graph synthesis and tolerable delay margin associated with the graphs, and present how one can build delay-tolerant graphs for coupled systems at hand. Finally, we calculate the largest achievable delay margin when tailoring multiple graphs together in order to understand large scale systems. This calculation becomes possible by utilizing the graphical nature of our previously developed Responsible Eigenvalue (RE) concept. Experimental results will be reported later in the future to explore the validity of our developments.