Identifying Network Structure of Linear Dynamical Systems: Observability and Edge Misclassification
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| Format: | Preprint |
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2025
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| _version_ | 1866911507566034944 |
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| author | Gill, Jaidev Li, Jing Shuang |
| author_facet | Gill, Jaidev Li, Jing Shuang |
| contents | This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this is a consideration often neglected by standard network inference methods. We show that the space of these networks are related through the nullspace of the observability matrix for the true network. We establish relevant metrics to investigate this space, including an analytic characterization of the most structurally dissimilar network that can be inferred, as well as the possibility of mis-inferring presence or absence of edges. In simulations, we find that when observing over 6\% of nodes in random network models (e.g., Erd\H os-R\' enyi and Watts-Strogatz), approximately 99\% of edges are correctly classified. Extending this discussion, we construct a family of networks that keep measurements $ε$-close to each other, and connect the identifiability of these networks to the spectral properties of an augmented observability Gramian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14065 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Identifying Network Structure of Linear Dynamical Systems: Observability and Edge Misclassification Gill, Jaidev Li, Jing Shuang Systems and Control Optimization and Control This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this is a consideration often neglected by standard network inference methods. We show that the space of these networks are related through the nullspace of the observability matrix for the true network. We establish relevant metrics to investigate this space, including an analytic characterization of the most structurally dissimilar network that can be inferred, as well as the possibility of mis-inferring presence or absence of edges. In simulations, we find that when observing over 6\% of nodes in random network models (e.g., Erd\H os-R\' enyi and Watts-Strogatz), approximately 99\% of edges are correctly classified. Extending this discussion, we construct a family of networks that keep measurements $ε$-close to each other, and connect the identifiability of these networks to the spectral properties of an augmented observability Gramian. |
| title | Identifying Network Structure of Linear Dynamical Systems: Observability and Edge Misclassification |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2509.14065 |