Sufficient condition for locally unidentifiable edge weights from any single-state trajectory in networked linear systems
In this study, we analyse the local identifiability of parameters in linear systems whose state matrix is given by a graph Laplacian. Graph Laplacian is a matrix given by a graph and the weights of its edges, where the weights represent the parameters in those systems. There are cases in which param...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-12-01
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| Series: | SICE Journal of Control, Measurement, and System Integration |
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| Online Access: | http://dx.doi.org/10.1080/18824889.2024.2315641 |
| _version_ | 1826935109620596736 |
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| author | Masafumi Yamakawa Toru Asai Ryo Ariizumi Shun-ichi Azuma |
| author_facet | Masafumi Yamakawa Toru Asai Ryo Ariizumi Shun-ichi Azuma |
| author_sort | Masafumi Yamakawa |
| collection | DOAJ |
| description | In this study, we analyse the local identifiability of parameters in linear systems whose state matrix is given by a graph Laplacian. Graph Laplacian is a matrix given by a graph and the weights of its edges, where the weights represent the parameters in those systems. There are cases in which parameter estimation has to be conducted with a single trajectory data. In this case, detecting whether the parameter is locally unidentifiable (non-locally identifiable (LI)) from a single-state trajectory a priori is important. This is because we need conditions to avoid estimating non-LI parameters. Therefore, we address a problem to find the condition which implies that the parameter is non-LI from any single-state trajectory. Then, we obtain a sufficient condition for the parameter to be non-LI from any single-state trajectory. The condition is given based on the number of vertices and edges of the graph and the number of distinct eigenvalues of the graph Laplacian. This paper also presents an example that satisfies the condition. |
| first_indexed | 2024-03-07T23:47:20Z |
| format | Article |
| id | doaj.art-91bc1496f85444d588204384dd7a5176 |
| institution | Directory Open Access Journal |
| issn | 1884-9970 |
| language | English |
| last_indexed | 2025-02-17T18:00:02Z |
| publishDate | 2024-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | SICE Journal of Control, Measurement, and System Integration |
| spelling | doaj.art-91bc1496f85444d588204384dd7a51762024-12-13T15:19:03ZengTaylor & Francis GroupSICE Journal of Control, Measurement, and System Integration1884-99702024-12-01171808610.1080/18824889.2024.23156412315641Sufficient condition for locally unidentifiable edge weights from any single-state trajectory in networked linear systemsMasafumi Yamakawa0Toru Asai1Ryo Ariizumi2Shun-ichi Azuma3Nagoya UniversityNagoya UniversityTokyo University of Agriculture and TechnologyKyoto UniversityIn this study, we analyse the local identifiability of parameters in linear systems whose state matrix is given by a graph Laplacian. Graph Laplacian is a matrix given by a graph and the weights of its edges, where the weights represent the parameters in those systems. There are cases in which parameter estimation has to be conducted with a single trajectory data. In this case, detecting whether the parameter is locally unidentifiable (non-locally identifiable (LI)) from a single-state trajectory a priori is important. This is because we need conditions to avoid estimating non-LI parameters. Therefore, we address a problem to find the condition which implies that the parameter is non-LI from any single-state trajectory. Then, we obtain a sufficient condition for the parameter to be non-LI from any single-state trajectory. The condition is given based on the number of vertices and edges of the graph and the number of distinct eigenvalues of the graph Laplacian. This paper also presents an example that satisfies the condition.http://dx.doi.org/10.1080/18824889.2024.2315641parameter estimationlocal identifiabilitylinear systemgraph laplacianundirected graph |
| spellingShingle | Masafumi Yamakawa Toru Asai Ryo Ariizumi Shun-ichi Azuma Sufficient condition for locally unidentifiable edge weights from any single-state trajectory in networked linear systems SICE Journal of Control, Measurement, and System Integration parameter estimation local identifiability linear system graph laplacian undirected graph |
| title | Sufficient condition for locally unidentifiable edge weights from any single-state trajectory in networked linear systems |
| title_full | Sufficient condition for locally unidentifiable edge weights from any single-state trajectory in networked linear systems |
| title_fullStr | Sufficient condition for locally unidentifiable edge weights from any single-state trajectory in networked linear systems |
| title_full_unstemmed | Sufficient condition for locally unidentifiable edge weights from any single-state trajectory in networked linear systems |
| title_short | Sufficient condition for locally unidentifiable edge weights from any single-state trajectory in networked linear systems |
| title_sort | sufficient condition for locally unidentifiable edge weights from any single state trajectory in networked linear systems |
| topic | parameter estimation local identifiability linear system graph laplacian undirected graph |
| url | http://dx.doi.org/10.1080/18824889.2024.2315641 |
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