Dynamic Optimal Control: A Real-Time Control Optimization Algorithm for Dynamic Networks

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.