Global network control from local information

Area of Science:

• Control Theory
• Network Systems
• Complex Systems

Background:

• Classical network control relies on global state information.
• Real-time global state reconstruction faces data collection, communication, and processing limitations.
• Need for efficient control strategies in large-scale networks with data constraints.

Purpose of the Study:

• Introduce a novel control approach using limited state information neighborhoods.
• Analyze the trade-off between control performance and neighborhood size.
• Investigate the role of the controllability Gramian's condition number.

Main Methods:

• Developed a control method based on local state information.
• Analyzed the theoretical relationship between neighborhood size and performance via the controllability Gramian.
• Conducted simulations on regular and random networks.
• Applied the method to power-grid synchronization control.

Main Results:

• Control actions can be computed using states within a limited neighborhood.
• The condition number of the controllability Gramian dictates the performance-neighborhood size trade-off.
• Simulations confirm theoretical findings on various network types.
• Power-grid synchronization control demonstrated the practical applicability.

Conclusions:

• Efficient control of large networks is possible using only local information.
• Reducing the state information neighborhood size has minimal impact on control performance for well-conditioned Gramians.
• This approach overcomes limitations of real-time global state reconstruction.