Functional observability and target state estimation in large-scale networks

Area of Science:

• Complex Systems
• Network Science
• Control Theory

Background:

• Quantitative understanding and control of complex dynamical systems rely on observing internal states.
• Large-scale networks often lack sufficient sensors for full state observability.
• High dimensionality limits the computational feasibility of full-state observers.

Purpose of the Study:

• To develop a graph-based theory of functional observability for complex dynamical systems.
• To create scalable algorithms for determining minimal sensor sets and designing minimum-order observers.
• To enable state reconstruction from limited measurements in large-scale networks.

Main Methods:

• Developed a graph-based theory of functional observability.
• Created algorithms to identify minimal sensor requirements.
• Designed minimum-order state observers for functional observation.
• Applied methods to power grid cyberattack detection and epidemic prevalence inference.

Main Results:

• Functional observability allows targeted state reconstruction from limited measurements.
• Algorithms efficiently determine minimal sensor sets and design observers.
• Functional observers achieve high estimation quality with reduced sensing and computation.
• Methods are scalable to large dynamical networks.

Conclusions:

• Functional observability overcomes the curse of dimensionality in large-scale systems.
• The proposed methods offer a scalable solution for analyzing otherwise inaccessible dynamical processes.
• This approach enhances capabilities in areas like cyberattack detection and epidemic monitoring.