Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Data-driven Control of Hypergraphs: Leveraging THIS to Damp Noise in Diffusive Hypergraphs

Robin Delabays, Yuanzhao Zhang, Florian Dörfler, Giulia De Pasquale

TL;DR

This work addresses controlling systems with higher-order interactions where the topology is not fully observed. It couples a data-driven hypergraph inference method, THIS, with a parsimonious leaf-node droop controller to steer a diffusive hypernetwork toward a desired equilibrium $x^*$. The authors formalize a hypergraph analogue of structural controllability and validate the approach on a 10-node, third-order Kuramoto model, showing that leaf nodes can be reliably identified and controlled even when edge-level inference is imperfect. The results demonstrate a practical, end-to-end, data-driven route to control higher-order networked systems with partial observations, with potential impact in engineered and biological hypernetworks.

Abstract

Controllability determines whether a system's state can be guided toward any desired configuration, making it a fundamental prerequisite for designing effective control strategies. In the context of networked systems, controllability is a well-established concept. However, many real-world systems, from biological collectives to engineered infrastructures, exhibit higher-order interactions that cannot be captured by simple graphs. Moreover, the way in which agents interact and influence one another is often unknown and must be inferred from partial observations of the system. Here, we close the loop between a hypergraph representation and our recently developed hypergraph inference algorithm, THIS, to infer the underlying multibody couplings. Building on the inferred structure, we design a parsimonious controller that, given a minimal set of controllable nodes, steers the system toward a desired configuration. We validate the proposed system identification and control framework on a network of Kuramoto oscillators evolving over a hypergraph.

Data-driven Control of Hypergraphs: Leveraging THIS to Damp Noise in Diffusive Hypergraphs

TL;DR

This work addresses controlling systems with higher-order interactions where the topology is not fully observed. It couples a data-driven hypergraph inference method, THIS, with a parsimonious leaf-node droop controller to steer a diffusive hypernetwork toward a desired equilibrium . The authors formalize a hypergraph analogue of structural controllability and validate the approach on a 10-node, third-order Kuramoto model, showing that leaf nodes can be reliably identified and controlled even when edge-level inference is imperfect. The results demonstrate a practical, end-to-end, data-driven route to control higher-order networked systems with partial observations, with potential impact in engineered and biological hypernetworks.

Abstract

Controllability determines whether a system's state can be guided toward any desired configuration, making it a fundamental prerequisite for designing effective control strategies. In the context of networked systems, controllability is a well-established concept. However, many real-world systems, from biological collectives to engineered infrastructures, exhibit higher-order interactions that cannot be captured by simple graphs. Moreover, the way in which agents interact and influence one another is often unknown and must be inferred from partial observations of the system. Here, we close the loop between a hypergraph representation and our recently developed hypergraph inference algorithm, THIS, to infer the underlying multibody couplings. Building on the inferred structure, we design a parsimonious controller that, given a minimal set of controllable nodes, steers the system toward a desired configuration. We validate the proposed system identification and control framework on a network of Kuramoto oscillators evolving over a hypergraph.

Paper Structure

This paper contains 11 sections, 2 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Notation and Preliminaries
  3. Hypergraphs
  4. Higher-order Kuramoto model
  5. Hypergraph Stabilization via Noise Rejection
  6. Identification and Control Algorithm
  7. Initialization and State Space Exploration
  8. System Identification via THIS
  9. Droop Controller Design
  10. Mathematical Simulations
  11. Conclusions

Figures (3)

  • Figure 1: Examples of hypergraphs. In the left panel, nodes 2 and 3 are leaves and need to be controlled. In the middle panel, only node 2 is a leaf and needs to be controlled. In the right panel, there is no leaf node and one needs to control any one of the three nodes.
  • Figure 2: Algorithm process pipeline: In phase 1) trajectories are collected for a system operating in the vicinity of a locally stable equilibrium point for a time interval $[t_0,t_1]$; at time instant $t_2$ phase 2 starts, where THIS is applied to infer the hypergraph topology, after which, at phase 3) the minimal set of controllable nodes is detected and the system driven towards the desired equilibrium point $x^*$.
  • Figure 3: Top panel: Trajectory of the 10 agents of a 3rd-order Kuramoto model on a random 3-hypergraph. Each agent deviates from its steady state due to noise. Bottom panel: The time series of the nodes over the first 5 time units are used to infer the hypergraph structure using THIS. Within this hypergraph, the leaf nodes are identified and a proportional control is applied to them, starting at time $t_2=5.5$. From $t_0=0$ to $t_2=5.5$, the two time series are exactly the same.

Theorems & Definitions (2)

  • Definition 1: Structural Controllability
  • Definition 2: Minimal Set of Controllable Nodes