In many complex systems, elements interact via time-varying network topologies. Recent research shows that temporal correlations in the chronological ordering of interactions crucially influence network properties and dynamical processes. How these correlations affect our ability to control systems with time-varying interactions remains unclear. In this work, we use higher-order network models to extend the framework of structural controllability to temporal networks, where the chronological ordering of interactions gives rise to time-respecting paths with non-Markovian characteristics. We study six empirical data sets and show that non-Markovian characteristics of real systems can both increase or decrease the minimum time needed to control the whole system. With both empirical data and synthetic models, we further show that spectral properties of generalisations of graph Laplacians to higher-order networks can be used to analytically capture the effect of temporal correlations on controllability. Our work highlights that (i) correlations in the chronological ordering of interactions are an important source of complexity that significantly influences the controllability of temporal networks, and (ii) higher-order network models are a powerful tool to understand the temporal-topological characteristics of empirical systems.

在许多复杂的系统中，元素通过时变的网络拓扑进行交互。最近的研究表明，相互作用的时间顺序中的时间相关性对网络特性和动力学过程具有至关重要的影响。这些相关性如何影响我们通过时变相互作用控制系统的能力仍不清楚。在这项工作中，我们使用高阶网络模型将结构可控性的框架扩展到时间网络，其中交互的时间顺序产生了具有非马尔可夫特性的时效路径。我们研究了六个经验数据集，结果表明，实际系统的非马尔可夫特性可以增加或减少控制整个系统所需的最短时间。借助经验数据和综合模型，我们进一步表明，将图拉普拉斯算子推广到高阶网络的频谱特性可用于分析性地捕获时间相关性对可控性的影响。我们的工作着重指出（i）交互作用的时间顺序相关性是复杂性的重要来源，它显着影响时间网络的可控性，并且（ii）高阶网络模型是了解时间序列网络拓扑特性的有力工具。经验系统。