Functional observability and target state estimation in large-scale networks

TL;DR

This paper introduces a graph-based theory of functional observability for large-scale networks, enabling targeted state estimation with fewer sensors and computational resources, demonstrated through power grid and epidemic applications.

Contribution

It develops scalable algorithms for minimal sensor placement and low-order functional observer design in large networks, addressing high-dimensionality challenges.

Findings

Functional observability allows targeted state reconstruction with fewer sensors.

Proposed methods scale to large networks and reduce computational complexity.

Applications include cyber-attack detection and epidemic prevalence estimation.

Abstract

The quantitative understanding and precise control of complex dynamical systems can only be achieved by observing their internal states via measurement and/or estimation. In large-scale dynamical networks, it is often difficult or physically impossible to have enough sensor nodes to make the system fully observable. Even if the system is in principle observable, high-dimensionality poses fundamental limits on the computational tractability and performance of a full-state observer. To overcome the curse of dimensionality, we instead require the system to be functionally observable, meaning that a targeted subset of state variables can be reconstructed from the available measurements. Here, we develop a graph-based theory of functional observability, which leads to highly scalable algorithms to i) determine the minimal set of required sensors and ii) design the corresponding state observer of minimum order. Compared to the full-state observer, the proposed functional observer achieves the same estimation quality with substantially less sensing and computational resources, making it suitable for large-scale networks. We apply the proposed methods to the detection of cyber-attacks in power grids from limited phase measurement data and the inference of the prevalence rate of infection during an epidemic under limited testing conditions. The applications demonstrate that the functional observer can significantly scale up our ability to explore otherwise inaccessible dynamical processes on complex networks.