In this paper, we develop a notion of controllability for hypergraphs via tensor algebra and polynomial control theory. Inspired by uniform hypergraphs, we propose a new tensor-based multilinear dynamical system representation, and derive a Kalman-rank-like condition to determine the minimum number of control nodes (MCN) needed to achieve controllability of even uniform hypergraphs. We present an efficient heuristic to obtain the MCN. MCN can be used as a measure of robustness, and we show that it is related to the hypergraph degree distribution in simulated examples. Finally, we use MCN to examine robustness in real biological networks.

中文翻译：

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超图的可控性

在本文中，我们通过张量代数和多项式控制理论开发了超图的可控性概念。受均匀超图的启发，我们提出了一种新的基于张量的多线性动力系统表示，并推导出类卡尔曼秩条件来确定实现均匀超图可控性所需的最小控制节点 (MCN) 数量。我们提出了一种有效的启发式方法来获得 MCN。MCN 可以用作稳健性的度量，我们证明它与模拟示例中的超图度分布有关。最后，我们使用 MCN 来检查真实生物网络中的鲁棒性。