Closed-loop control of higher-order complex networks: Finite-time and pinning strategies

Increasing evidences have demonstrated the essentiality of many-body interactions in modeling various systems in physics, biology, and social sciences. Control strategies are useful tools to steer real-world complex systems to desired targets. Existing works focus on open-loop control, which relies on predefined control signals, and closed-loop control, which requires an infinite-time duration, on conventional networks expressed by graphs. This work designs closed-loop controllers for higher-order complex networks characterized by simplicial complexes. Protocols including the linear feedback controller and a switching controller, which is a combination of a linear controller and a finite-time controller, are first adapted to higher-order networks to realize successful control tasks, with the rigorous upper bound of the control time theoretically derived and compared. Extensive numerical simulations on benchmark and real-world higher-order complex networks demonstrate the effectiveness of the control protocols and further provide insights on pinning control strategy to higher-order networks. These results shed light on a comprehensive discovery of controlling higher-order complex networks and have also applied values.