Optimal pinning control of directed hypergraphs

TL;DR

This paper studies how to control directed hypergraph networks by selecting key nodes to pin, providing theoretical conditions for control success and a heuristic method that outperforms existing approaches.

Contribution

It extends pinning control theory from digraphs to directed hypergraphs with higher-order interactions and proposes a novel heuristic for node selection.

Findings

Derived necessary and sufficient conditions for control via pinning.

Proposed a greedy heuristic that outperforms existing methods.

Validated the effectiveness of the approach through simulations.

Abstract

Identifying the nodes that must be directly controlled to steer a network along a desired trajectory remains an open problem for digraphs, and even more so for hypergraphs. In this manuscript, we investigate network systems coupled via directed hypergraphs and consider a broad class of individual dynamics and coupling configurations, extending the definition of type II networks originally formulated for digraphs. For this class of networks with higher-order interactions, we establish necessary and sufficient conditions under which a pinning selection locally ensures successful control. Building on these analytical results, we propose a greedy heuristic for pinning control selection, which demonstrably outperforms existing methods.