Controllability and Observability of Temporal Hypergraphs

TL;DR

This paper extends the concepts of controllability and observability to temporal hypergraphs, providing tensor-based criteria to analyze complex, time-varying systems like ecological and social networks.

Contribution

It introduces a novel tensor-based framework for assessing controllability and observability in dynamic hypergraph models, addressing a gap in existing static hypergraph analysis methods.

Findings

Tensor-based rank conditions determine weak controllability.

Tensor-based rank conditions determine weak observability.

Framework validated with synthetic and real-world data.

Abstract

Numerous complex systems, such as those arisen in ecological networks, genomic contact networks, and social networks, exhibit higher-order and time-varying characteristics, which can be effectively modeled using temporal hypergraphs. However, analyzing and controlling temporal hypergraphs poses significant challenges due to their inherent time-varying and nonlinear nature, while most existing methods predominantly target static hypergraphs. In this article, we generalize the notions of controllability and observability to temporal hypergraphs by leveraging tensor and nonlinear systems theory. Specifically, we establish tensor-based rank conditions to determine the weak controllability and observability of temporal hypergraphs. The proposed framework is further demonstrated with synthetic and real-world examples.