# Controllability of Coarsely Measured Networked Linear Dynamical Systems (Extended Version)

arXiv: https://arxiv.org/abs/2206.10569 · HTML: https://mlsanity.com/paper/2206.10569/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 66 references that are in the map.
- First posted on arXiv 21 Jun 2022.

## Builds on (most cited first, 24 of 24)

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Learning Latent Block Structure in Weighted Networks](https://mlsanity.com/paper/1404.0431/) (2014)
- [Estimating Mixed Memberships with Sharp Eigenvector Deviations](https://mlsanity.com/paper/1709.00407/) (2017)
- [Multi-scale brain networks](https://mlsanity.com/paper/1608.08828/) (2016)
- [Controllability of Brain Networks](https://mlsanity.com/paper/1406.5197/) (2014)
- [Controllability Metrics, Limitations and Algorithms for Complex Networks](https://mlsanity.com/paper/1308.1201/) (2013)
- [On Submodularity and Controllability in Complex Dynamical Networks](https://mlsanity.com/paper/1404.7665/) (2014)
- [The Geometric Block Model](https://mlsanity.com/paper/1709.05510/) (2017)
- [Blind identification of stochastic block models from dynamical observations](https://mlsanity.com/paper/1905.09107/) (2019)
- [Exact Controllability of Complex Networks](https://mlsanity.com/paper/1310.5806/) (2013)
- [Node-Centric Graph Learning from Data for Brain State Identification](https://mlsanity.com/paper/2011.02179/) (2020)
- [Model Reduction Methods for Complex Network Systems](https://mlsanity.com/paper/2012.02268/) (2020)
- [Minimal Controllability Problems](https://mlsanity.com/paper/1304.3071/) (2013)
- [Submodularity of Energy Related Controllability Metrics](https://mlsanity.com/paper/1403.6351/) (2014)
- [A practical guide to methodological considerations in the controllability of structural brain networks](https://mlsanity.com/paper/1908.03514/) (2019)
- [A Hierarchical Graph Signal Processing Approach to Inference from Spatiotemporal Signals](https://mlsanity.com/paper/2010.13164/) (2020)
- [Graph Community Detection from Coarse Measurements: Recovery Conditions for the Coarsened Weighted Stochastic Block Model](https://mlsanity.com/paper/2102.13135/) (2021)
- [Minimum Cost Input/Output Design for Large Scale Linear Structural Systems](https://mlsanity.com/paper/1407.3327/) (2014)
- [Minimal Actuator Placement with Bounds on Control Effort](https://mlsanity.com/paper/1409.3289/) (2014)
- [Controllability Gramian Spectra of Random Networks](https://mlsanity.com/paper/1609.04727/) (2016)
- [Reduction of Second-Order Network Systems with Structure Preservation](https://mlsanity.com/paper/1706.01751/) (2017)
- [Clustering-Based Model Order Reduction for Nonlinear Network Systems](https://mlsanity.com/paper/2003.06952/) (2020)
- [Controllability Analysis of Functional Brain Networks](https://mlsanity.com/paper/2003.08278/) (2020)
- [Community Detection for Gossip Dynamics with Stubborn Agents](https://mlsanity.com/paper/2003.14028/) (2020)

## Abstract (arXiv)

We consider the controllability of large-scale linear networked dynamical systems when complete knowledge of network structure is unavailable and knowledge is limited to coarse summaries. We provide conditions under which average controllability of the fine-scale system can be well approximated by average controllability of the (synthesized, reduced-order) coarse-scale system. To this end, we require knowledge of some inherent parametric structure of the fine-scale network that makes this type of approximation possible. Therefore, we assume that the underlying fine-scale network is generated by the stochastic block model (SBM) -- often studied in community detection. We then provide an algorithm that directly estimates the average controllability of the fine-scale system using a coarse summary of SBM. Our analysis indicates the necessity of underlying structure (e.g., in-built communities) to be able to quantify accurately the controllability from coarsely characterized networked dynamics. We also compare our method to that of the reduced-order method and highlight the regimes where both can outperform each other. Finally, we provide simulations to confirm our theoretical results for different scalings of network size and density, and the parameter that captures how much community-structure is retained in the coarse summary.