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.

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

References in corpus (26)

• Emergence of scaling in random networks
• Synchronization in complex networks
• Renormalization group analysis of the small-world network model
• Prediction and predictability of global epidemics: the role of the airline transportation network
• The Kuramoto model in complex networks
• Synchronization in Complex Oscillator Networks and Smart Grids
• Realistic Control of Network Dynamics
• Small vulnerable sets determine large network cascades in power grids
• Structure-based control of complex networks with nonlinear dynamics
• Nodal dynamics, not degree distributions, determine the structural controllability of complex networks
• Controllability analysis of the directed human protein interaction network identifies disease genes and drug targets
• Comparative analysis of existing models for power-grid synchronization
• A Distributed Observer for a Time-Invariant Linear System
• Controllability transition and nonlocality in network control
• Modeling, state estimation, and optimal control for the US COVID-19 outbreak
• Optimal, near-optimal, and robust epidemic control
• Energy Scaling of Targeted Optimal Control of Complex Networks
• Networkcontrology
• Power-law distribution in the number of confirmed COVID-19 cases
• Structural, Dynamical and Symbolic Observability: From Dynamical Systems to Networks
• State observation and sensor selection for nonlinear networks
• Cyber-physical risks of hacked Internet-connected vehicles
• Functional target controllability of networks: structural properties and efficient algorithms
• Observability and Synchronization of Neuron Models
• Limits on reconstruction of dynamical networks
• Particle filtering of dynamical networks: Highlighting observability issues

Cited by in corpus (10)

• The low-rank hypothesis of complex systems
• Prevalence and scalable control of localized networks
• Functional Observability, Structural Functional Observability and Optimal Sensor Placement
• 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