Real-world complex network systems often experience changes over time, and controlling their state has important applications in various fields. While external control signals can drive static networks to a desired state, dynamic networks have varying topologies that require changes to the driver nodes for maintaining control. Most existing approaches require knowledge of topological changes in advance to compute optimal control schemes. However, obtaining such knowledge can be difficult for many real-world dynamic networks. To address this issue, we propose a novel real-time control optimization algorithm called Dynamic Optimal Control (DOC) that predicts node control importance using historical information to minimize control scheme changes and reduce overall control cost. We design an efficient algorithm that fine-tunes the current control scheme by repairing past maximum matching to respond to changes in the network topology. Our experiments on real and synthetic dynamic networks show that DOC significantly reduces control cost and achieves more stable and focused real-time control schemes compared to traditional algorithms. The proposed algorithm has the potential to provide solutions for real-time control of complex dynamic systems in various fields.

翻译：现实世界中的复杂网络系统常常随时间变化，控制其状态在多个领域具有重要应用。尽管外部控制信号可以驱动静态网络达到期望状态，但动态网络拓扑结构的不断变化要求调整驱动节点以维持控制能力。现有方法大多需要预先获知拓扑变化信息才能计算最优控制方案，然而对于许多真实动态网络而言，获取此类信息颇具难度。为解决该问题，本文提出一种名为动态最优控制（DOC）的新型实时控制优化算法，该算法利用历史信息预测节点控制重要性，从而最小化控制方案变动并降低总体控制成本。我们设计了一种高效算法，通过修复历史最大匹配来微调当前控制方案，以响应网络拓扑变化。在真实与合成动态网络上的实验表明，与传统算法相比，DOC能显著降低控制成本，并实现更稳定、更聚焦的实时控制方案。该算法有望为多领域复杂动态系统的实时控制提供解决方案。