Causality-Aware Pinning Control for Fixed-Time and Predefined-Time Synchronization of Multi-Link Directed Hypergraphs

Pinning control provides a practical and cost-saving means to control hypergraph networks. However, most existing studies on hypergraph networks are restricted to static topologies and often overlook dynamic causal interactions, limiting the effective selection of pinned nodes in practical scenarios. Motivated by these, this paper proposes a novel multi-link directed hypergraph (MDH) and a causality-aware pinning control (CAPC) scheme to ensure fixed/predefined-time synchronization. Specifically, a MDH with time-varying higher-order structures is constructed to characterize dynamic, multi-weight, and directed interactions among nodes. Moreover, to adapt to the time-varying and higher-order properties of the MDH, CAPC is introduced to dynamically identify energy-efficient pinned nodes based on causal relationships in higher-order networks. Finally, based on the data-driven selected pinned nodes, sufficient conditions for the design of adaptive fixed/predefined-time pinning controllers are rigorously derived. Numerical simulations and a secure communication application further validate the effectiveness of the proposed approach in resource-constrained environments.