Functional observability and target state estimation in large-scale networks

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.

Codes are available in GitHub (https://github.com/montanariarthur/FunctionalObservability)

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Cited by in corpus (10)

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• Prevalence and scalable control of localized networks
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• Functional observability and subspace reconstruction in nonlinear systems
• Duality between controllability and observability for target control and estimation in networks
• Target Controllability and Target Observability of Structured Network Systems
• On the Popov-Belevitch-Hautus tests for functional observability and output controllability
• Observing network dynamics through sentinel nodes
• Optimal flock formation induced by agent heterogeneity
• On sample-based functional observability of linear systems